VOLUME V ISSUE 1 NEWS 2019
TATA INSTITUTE OF FUNDAMENTAL RESEARCH
photograph by Peter Badge | www.abelprize.no
Wall plaque at the ICTS Campus, Bangalore.
REMEMBERING MICHAEL ATIYAH ICTS Address Survey No. 151, Shivakote village, Hesaraghatta Hobli, North Bengaluru, India 560089 Website www.icts.res.in 1
VOLUME V NEWS ISSUE 1 2019
TATA INSTITUTE OF FUNDAMENTAL RESEARCH
L R: C. Musili, C.S. Seshadri, M.S. Narasimhan, M.S. Raghunathan and David Mumford at TIFR (1968) ⟶ www.cmi.ac.in/~ramadas/NS@50/ tifr archives
Michael Atiyah lecturing at TIFR tifr archives Michael Atiyah during his visit to TIFR, Mumbai, in 1984. MICHAEL ATIYAH M.S. NARASIMHAN & C.S. SESHADRI
M.S. NARASIMHAN mathematical aspects of gauge theory arising in of holomorphic vector bundles on the Riemann Sir Michael Atiyah was a great mathematician theoretical physics. surface which have been studied earlier by Seshadri who made path-breaking contributions to various and myself. This work of Atiyah and Bott was very His best known result is the celebrated Atiyah- fields in mathematics and played a crucial role in influential and popularised these moduli spaces Singer index theorem, which is a vast generalisation promoting the resurgence of contact between among physicists. of famous results like the Riemann-Roch theorem mathematics and theoretical physics in the latter and which is intimately related to K-Theory. A He had an effervescent and inspiring personality. half of the twentieth century. major related work is the Atiyah-Patodi-Singer He valued collaboration in mathematics and loved He was the recipient of many honours, including index theorem, which deals with elliptic operators intense mathematical discussions. He seemed to the Fields Medal and the Abel Prize. His work on manifolds with boundary and non-local derive many of his insights and ideas in the process combined creatively Analysis, Differential boundary conditions. (A version of the Hirzebruch of talking. Geometry and Topology. His major contributions signature theorem for manifolds with boundary) I maintained a close and fruitful contact with him have been to Topological K-Theory (which proved Atiyah and Bott made an extensive study of over the years and we had several conversations to be a remarkably powerful tool in Topology), the Yang-Mills equation on compact Riemann on moduli problems and some aspects of the index Index Theorem for linear elliptic operators and surfaces and its relationship to the moduli spaces theorem. Moreover, many of my best students did
www.icts.res.in 2 | ICTS NEWS | VOLUME V | ISSUE 1 2019 3 their post-doctoral study with Atiyah, the best C.S. SESHADRI earliest to perceive the importance of NS and let his “… The fact that I had physics friends is an known example being Vijay K. Patodi. Patodi’s I had heard of Michael Atiyah as a brilliant student student Newstead to calculate the cohomology of indication that the frontiers between disciplines stay in Princeton, working with Atiyah, resulted of Hodge when I was a graduate student at the certain “moduli spaces” figuring in NS. Theory needs were breaking down, and this has become the in his celebrated joint work with Atiyah, Bott and Tata Institute of Fundamental Research (TIFR). main feature of our times. The old rigid disciplines Newstead got a position in Liverpool and a framework Singer. (Atiyah and I later edited the Collected of the past are giving way to a much more fluid Then I came across his paper on the classification of Atiyah arranged for a visit to Liverpool by Papers of Patodi. In the foreword Atiyah wrote in which to scene, which is why the ICTS is the right body for vector bundles on Elliptic Curves. This attracted me M. S. Narasimhan and me. Atiyah again perceived that the work of Atiyah-Patodi-Singer ‘was the future. The future belongs to the young and the since Grothendieck had classified vector bundles on the importance of “moduli spaces of parabolic a great collaboration, exploiting the different develop and, as a science that is now emerging will affect the lives of the projective line and I noticed in my thesis that vector bundles” – a work I had done with Vikram talents of the participants.’) everyone on the planet. The ICTS has a noble task, ’s result is a consequence of an early Mehta (i.e. the geometry and physics of knots, Grothendieck mathematician, that of providing the right atmosphere to inspire I will mention a few recollections of my work of G.D. Birkoff. by Atiyah). I met Atiyah several times during the next generation of scientists …” ■ mathematical interactions with him. The original 1975–76, at the Institute for Advanced Study, I believe that In 1957, I proved that a finitely generated proof of the Atiyah-Bott fixed point theorem Princeton, TIFR Colloquium on vector bundles, Read the full text of the speeches here: projective module over the ring of polynomials mathematics used a result of Takeshi Kotake and myself on 1982, sometime in Bonn when he expressed his https://bit.ly/Atiyah_ScienceAtICTS_Speech in two variables is free (the first non-trivial case fractional powers of linear elliptic operators. great regard for Patodi. provides https://bit.ly/Atiyah_ScienceAtICTS_youtube of Serre’s problem). I attended the International Atiyah asked me to give a talk on this result. On https://bit.ly/Atiyah_FoundationStoneRemarks Congress held at Edinburgh in 1958 and remember It is a great privilege for having known Atiyah and another occasion, during an Arbeitstagung in that unifying conversing with during a cruise trip at this to have had his interest in my work. ■ Bonn, I told him about the canonical filtration Atiyah Congress. He told me that a British mathematician Michael Atiyah delivers the ceremonial speech for framework … which Harder and I had introduced on vector M. S. Narasimhan and C. S. Seshadri are eminent the ICTS Inauguration Event: Science at ICTS (whose name I forget) also solved Serre’s problem bundles on curves and suggested that it could mathematicians, well known for the famous for two variables but found that I had already was a nice problem that taught me that at times be of use in the work on Yang-Mills equation on Narasimhan-Seshadri theorem.They were among will contain mathematically oriented scientists. Spenta R. Wadia is a theoretical physicist and the done this earlier. Atiyah was the star attraction in a path integral it is necessary to sum over both Riemann surfaces he was undertaking at that the main pillars of the famed School of Mathematics So the exact allocation is not important, so long as Founding Director, Infosys Homi Bhabha Chair at the International Conference on Differential stable and unstable classical solutions to obtain the flexibility and quality are maintained. time with Bott. of TIFR, where they spent most of their professional Professor and Professor Emeritus at ICTS–TIFR, Analysis in 1964 at TIFR. A few months later, the correct answer. I did not publish this result as my life. Narasimhan later spent some years building Bengaluru His passing is a great loss for the mathematical Narasimhan-Seshadri theorem (NS) was proved. Finally, I totally agree that your initial appointments mathematics at ICTP and Seshadri founded the PhD mentor Bunji Sakita had emphasized that one community. M.S. Narasimhan gave a talk at this conference should be made cautiously and not in haste.” Chennai School of Mathematics. should write up only very substantive papers! In on an ingredient of NS. Atiyah was among the retrospect I think it would have been been valuable He embraced the idea and purpose of the ICTS, which to publish this simple result. he put forth in his remarks for the Foundation Stone BETWEEN THE Ceremony of ICTS on 28 December 2009, Michael also played an important role in the SCIENCE “Science has the noble aim of trying to understand establishment of the ICTS. The committee he the natural world in human terms: to make sense chaired that reviewed Mathematics at the Tata REMEMBERING MICHAEL FRANCIS ATIYAH of what we see. This brief phrase encapsulates both Institute of Fundamental Research (TIFR) in 2005 ABHIRUP GHOSH’ s submission towards theory and experiment. What we see, in the broad made a strong recommendation for an interactive the Augmenting Writing Skills for Articulating sense, covers experiment and making sense is the program for physicists and mathematicians. This Research (AWSAR) Award 2018, organised by (1929-2019) task of theory. As the great French mathematician reinforced the recommendation of the Theoretical the Department of Science and Technology Henri Poincare said, science is no more a collection of SPENTA R. WADIA Physics review committee in 2006 to establish ICTS (DST), Government of India, has been facts than a house is a collection of bricks: it requires in 2007. selected among the top 100 entries.. theory to hold it together. Michael Francis Atiyah, one of the most significant 3-dimensional topology. String theory embodies He was deeply interested in bringing the math and He strongly supported the idea of creating the ICTS Theory needs a framework in which to develop and, ADHIP AGARWALA’s PhD thesis titled mathematicians of the second half of the 20th this essential unity in a natural way. physics communities together to talk and share. and was a member of its International Advisory as a mathematician, I believe that mathematics ‘Excursions in ill condensed quantum matter: century, passed away on 11th January 2019. His His enthusiasm was infectious. He attributed his Board from inception till his passing away. His active During my tenure at the Enrico Fermi Institute, provides that unifying framework … from amorphous topological insulators profound contributions to topology, geometry interest in physics to his collaborator and friend involvement and advice has been encouraging and Michael visited the University of Chicago for a to fractional spins’ has been selected by and mathematical physics earned him the highest Isa Singer, who also visited UC during Michael’s invaluable. Commenting on the structure of the I am sure that mathematics, in all its various aspects, couple of months. Someone (I think Nambu) had Springer to be published under the Springer mathematics honours, viz. the Fields Medal in visit. He believed physicists were bubbling with ICTS in a letter to me, dated 14 February 2009, he mentioned about my interests to him. When I met will play an important part in the future activities thesis series. Adhip is currently a postdoctoral 1966 and the Abel Prize in 2004, which he shared ideas, flying in jet planes that would crash every said, him, he was surprised about my gender because my of this Center. In the complex modern world with fellow at ICTS-TIFR. He was a PhD student at with Isadore Singer. His achievements are well now and then, while mathematicians were like sure “I dislike rigid departmental boundaries. They have first name ends in a vowel. He also thought my last the enormous challenges that we face, from climate IISc, Bangalore. summarised by the Abel Prize citation: “For footed old men with walking sticks … proof is the a habit of perpetuating old demarcations well name was Arabic! change to energy, from poverty to water shortages, discovery and proof of the index theorem, bringing business of the mathematician, the important thing beyond their ‘sell-by date’. science provides the bedrock on which we can build RUKMINI DEY has been awarded a Core together topology, geometry and analysis, and their Michael was interested in my work on the unitary are the ideas that come from physics. our future. I am sure that this Center will play its part As you know the most active scientific frontiers are Research Grant (CRG) of the SERB as outstanding role in building new bridges between matrix models and the large N phase transition. We in guiding both India and the wider world in the years He suggested that I work on a problem of deriving those which cross boundaries. I hope the structure Principal Investigator by the Department of mathematics and theoretical physics.” used to have several discussions. At some point, ahead.” the heat kernel for particle motion on the manifold of your Institute will be flexible and adaptable. Science and Technology, Govt. of India. to my great surprise, he mentioned that he did His enthusiasm to intertwine mathematics and of the unitary group U(N) using the Feynman path Michael Atiyah will be remembered with fondness not know what a Bessel function was! I found that In your tentative list of subject areas you allocate physics and in particular quantum physics and integral. By summing over all classical solutions, and gratitude by the institution he helped establish MANAS KULKARNI has been awarded the unbelievable but told him that he did not need to 6 faculty in mathematics. Given the widespread emphasise their symbiotic existence was infectious. both stable and unstable, and including the linear and strongly supported, and whose value and SERB Early Career Research award by the know Bessel functions. I learnt a wonderful lesson application of mathematics in the sciences I find An example of this, based in part by suggestions oscillations (Hessian) with appropriate phases one relevance he well understood. I end this note with Department of Science and Technology, Govt. here – that one does not need to know ‘everything’ this number quite small. On the other hand I from Michael, is Witten’s application of Chern- can reproduce the exact answer that can be easily Michael’s last address to ICTS on the inauguration of of India. to do outstanding work. imagine many of the other areas (e.g. string theory) Simons gauge theory to the theory of knots in obtained using the method of free fermions. This its new campus on 20th June 2015.
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× infinitely many equations in infinitely many variables. in the plane a vector (p) = (v (p), v (p)) 2. (iii) Loops f and g in can be deformed into each 1 2 This means that V and W are infinite dimensional. A point p is called a singular point of the system of other continuously if and only if deg ( f ) = 0 ⃗푣 ∈ ℝ ℂ
Then the index is only defined for operatorsT for differential equations if the vector vanishes at p0: deg (g ). In other words, the degree completely which ker( T ) and coker( T ) are finite dimensional. (p ) = 0. The index of at p is an integer that is determines the homotopy class of f. 0 0 ⃗푣 An operator is said to be Fredholm if it has this defined as follows. Choose a small loop going once ⃗푣 ⃗푣 (iv) For any integer n, there is a loop f with property. Unlike the finite dimensional case, it is counterclockwise around p0, such that: (i) does not clearly no longer possible to give a formula for the vanish anywhere on the loop, and (ii) the only point deg ( f) = n. ⃗푣 index in terms of the dimensions of V and W, and inside the loop where vanishes is p0. Associating A remarkable feature of the degree is that there in fact the index does depend on the operator T. to every point p on the loop the vector f(p) = (p) are a multitude of different ways of describing and ⃗푣 However, the robustness of the index still persists in at that point defines a loop in the space of non–zero computing it: ⃗푣 the following form: vectors, i.e., a map GEOMETRIC DESCRIPTION FACT: If a Fredholm operator T can be deformed f : S1 × We can give two equivalent descriptions: into a Fredholm operator T , i.e., if there is a path � 1 - Draw a ray from the origin that intersects f connecting T to T in the space of Fredholm oper- from the circle S to the space⟶ ℂ 2 – {0} of non–zero ators, then the index� of T equals the index of T . vectors, which we have identified with the set × of transversally and does not pass through a point ℝ � non-zero complex numbers. The index of at p is of self-intersection of f. Then count, with sign,the We can think of passing to the infinite dimensional ℂ0 defined to be the winding number of the loop f: the number of times the curve f intersects the ray. case as allowing the matrix A = ( a ) above to ⃗푣 To assign a sign to each intersection point, we ij number of times the loop winds counterclockwise become an infinite matrix. There is a special class around the origin in . For instance, if the loop winds use the "traffic rule of the right of way": a point of of infinite matrices called matrices. These Toeplitz 4 times counterclockwise and 7 times clockwise intersection gets a positive sign if the ray has the are matrices whose entries are 'constant along ℂ around the origin, then the winding number is –3. right of way and a minus sign if the loop f has the diagonals', i.e., matrices of the form If the vector represents a magnetic field, then right of way (following Indian traffic conventions). the winding number would be the net number of c c c ... ⃗푣 - Alternatively, replace f by the loop g : f f ; in 0 -1 -2 counterclockwise rotations performed by a compass other words we project the loop f onto the unit THE ATIYAH-SINGER INDEX A = c c c c needle when the compass is taken once around a � /∣ ∣ 1 0 -1 -2 circle S1 × by rescaling every vector in × so small loop enclosing p . c c c c ⋱ 0 that it becomes a unit vector. Approximate g by a 2 1 0 –1 ⊂ ℂ ℂ Poincaré's seminal work "Analysis Situs", which nearby differentiable map h. Now fix a point q in THEOREM 2004 Abel Laureates Isidore Singer and Michael Atiyah at the Norwegian Royal Palace, 2004 ⋱ appeared in 1895, marks the beginning of modern the circle such that the derivative of h does not PRANAV PANDIT photographer - Knut Falch/Scanpix | www.abelprize.no vanish at any point p that is mapped to q by h. To a Toeplitz matrix,⁞ one⋱ can⋱ associate ⋱ its symbol algebraic topology. There he studies the question of Finally, count with sign the number of points that which is the function defined by theLaurent series when curves in an arbitrary 'space' can be deformed are mapped to q by h. A point p contributes with a The Atiyah-Singer index theorem is one of the most without actually finding the solutions themselves. of solutions to the equation , into one another, introducing what we today call uniqueness Ax = b positive or negative sign depending on the sign of n ∞ the fundamental group of a topological space. He profound and beautiful mathematical discoveries The next few sections attempt to explain the while the second term contains information about A ( z ) cn z also introduced the main ideas of homology theory. the derivative of h at p. of the second half of the 20th century. It provides a meaning of these terms, and to elucidate the the existence of solutions to the same equation. n = - � �� The simplest of the results in Analysis Situs clarifies fundamental link between analysis and topology. content of the index theorem. One easily checks that the index does not change We can view the symbol as a complex∞ valued COMBINATORIAL DESCRIPTION 1 the notion of 'winding number' used in Poincaré's The discovery of this link has led to a tremendous under perturbations of A. Indeed, by a linear change function on a circle S enclosing the origin. It Approximate f by a piecewise linear path g. Then we The index of an operator previous work on the local index of a differential synthesis of ideas, and to synergistic activity bringing of variables y = f ( x , ... , x ) (i.e., by performing turns out that the operator defined byA is Fredholm modify g by adding or deleting edges that bound j j 1 m ⊂ ℂ equation, and can be summarized as follows: together ideas from algebraic topology, differential Consider a system of n linear equations in m elementary row and column operations on the matrix if and only if the symbol never takes the value triangles that do not contain {0} until g is reduced to geometry, functional analysis and operator algebras. unknowns: A), we can bring the system of equations into the zero. Below, we will see that there is a manifestly a simple form where the winding number is 'obvious'. (i) There is an integer deg ( f ), called the winding The purpose of this expository article is to convey m standard form y = 0, k = 1, ... , r for some r m. From topological formula for the index of the operator A We will not discuss the details here. k number or the degree of f, which measures the a x = 0 something of the flavor of the mathematics of the ij j this one immediately sees that dim ( U ) = m — r and in terms of the symbol. "number of times f winds around the origin". DIFFERENTIAL GEOMETRIC DESCRIPTION i = 1 ≤ index theorem and its ramifications, with a bare dim ( U* ) = n — r, and therefore ind ( A ) = m — n. � From celestial mechanics to algebraic Approximate f by a differentiable function g and then (ii) The integer is stable under small minimum of technical detail. with complex coefficients . A natural Thus, the index of A depends only on the number deg ( f ) i = 1, ..., n, aij topology define of equations and unknowns, and is completely perturbations of f: it does not change if we Topology is concerned with the study of those quantity of interest is the (maximal) number of 1 dg independent of the coefficientsa . Switching gears, we turn now to the topological deform f in a continuous manner. deg ( f ) linearly independent solutions to this system of ij 2 –1 g properties of 'shapes' that remain unchanged under th ��√ � side of the story. In the late 19 century, the 1 equations, i.e., the dimension dim ( U ) of the space � �S continuous deformations. Analysis involves the study In terms of abstract linear algebra, we can express French mathematician and physicist Henri Poincaré π of operators, such as the operator of differentiation, U of solutions. However, this quantity is not robust, all this as follows. The index of a linear operator T : in the following sense: small perturbations of the was interested in the question of the stability of that transform one function into another. At its core, V W between finite dimensional vector spaces is planetary orbits. In order to capture the qualitative coefficientsa can lead to jumps in dim ( U ). We can the Atiyah-Singer index theorem is a statement ij defined by behavior of systems of non-linear ordinary get around this problem as follows. Let A = (a ) be ⟶ relating the analysis of elliptic partial differential ij differential equations, such as those that describe the n×m matrix of coefficients, and letU * be the ind ( T ) = dim ( ker ( T ) ) — dim ( coker ( T ) ) operators to the topology of the space of invertible planetary motions, Poincaré introduced, in 1881, the orthogonal complement to the set of vectors b = (b , complex-valued matrices. It states that the analytic 1 where ker ( T ) is the kernel of T and coker ( T ) is the notion of the at a singular point of a system of ... , b ) for which the equation Ax = b has a solution. index index of an elliptic partial differential equation is m cokernel of T. The matrix A defines a linear operator two differential equations in two variables. A pair of Alternatively, we could defineU* to be the space of equal to the topological index of its symbol. The m n TA : V W , where V = and W = . The index of differential equations analytic index is a quantity that measures the solutions to the equation A*y = 0, where A* is the A as defined above coincides with the index ofT A, 'number of independent solutions' to a differential conjugate transpose of A. Then we can define the ⟶ ℂ ℂ = v (x , x ) and we have ind ( T ) = dim ( V ) — dim ( W ), which is 1 1 1 2 index of A to be the quantity A equation, while the topological index is a measure independent of . A � = v (x , x ) of the obstruction to deforming one shape into 2 2 1 2 ind (A) = dim (U ) — dim (U* ) another. The index theorem allows us to 'count' The situation becomes much more interesting when � is specified by associating to every pointp = (x1, x2) the solutions to a complicated differential equation The first term is a measure of the (failure of) there are infinitely many degrees of freedom, i.e., Figure 1: (From left to right) Vector fields with index 1, –1, and 2.
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ALGEBRAIC DESCRIPTION We would like to 'count' the number of linearly decades. sphere. Using Bott's theorem on the classication of of modern algebraic geometry. It is a higher Approximate f with a function g whose Fourier independent solutions to the partial differential maps f : S2n–1 GL (N, ) discussed above, we can dimensional analogue of the Riemann-Roch theorem, On the other hand, we could view × as the series is finite so that we can write equation T( ) = 0. In general, the space of solutions assign an integer to this data. This integer is called which 'counts' the number of analytic functions with group GL (1, ) of 1 × 1 invertible matrices with ⟶ ℂ n can be infinite dimensional, so in order for this ℂ the topological index of the elliptic partial differential a prescribed behavior of zeroes and poles in terms of k 휙 complex entries. From this point of view, a natural counting to make sense, we need to impose equation. a topological quantity involving the number of holes g ( z ) ak z ℂ generalization would be the study of the space k = –n additional conditions on our equation. This is where in the surface. The relevant elliptic operator here is �� continiuous maps A precise discussion of the topological index involves 1 ellipticity enters the game. To explain this notion, + , where is the Cauchy-Riemann operator z for z S . This formula defines a meromorphic the notion of K-theory. The K-theory K(X ) of a space * we need to introduce the symbol T ( x, ) of the f : Sn‑1 GL (N, ) acting̅ ̅ on a certain̅ bundle of differential forms. / ̅ function on the unit disc { z z 1}. Then the bears to the collection Vect(X ) of vector bundles 휕 휕 휕 휕 휕 ∈ ⊂ ℂ differential operator T, which is the homogeneous degree of f is given by the formula 휎 휉 on X the same relation that integers bear to natural There are several other important applications ∈ ℂ | | | � polynomialof degree r in d variables given by the from the (n–1)-sphere to⟶ the spaceℂ of N × N numbers. Just as integers can be viewed as formal of the index theorem that we do not have space deg(f) = { Zeroes of g } - # { Poles of g } formula invertible matrices with complex entries. Given how # difficult it is to understand the space of continuous dierences n – m of natural numbers, elements of to discuss here, including the index theorem for where the zeroes and poles that are counted are Figure 2: Computing the winding number using T ( x, ) = a maps between spheres, it is quite surprising that this K(X ) are formal differences [E ] – [F ] of vector Dirac operators which is important in physics, and 훼 those that are contained in the unit disc. the geometric description. This curve has winding r 훼 question was almost completely settled by Raoul Bott bundles. K-theory is a vast subject in its own right, the Hirzebruch signature theorem, which plays an 휎 휉 � 휉 and the mathematics of the index theorem was one important role in cobordism theory (which in turn is number -1 = 1 -1 -1. |훼| = as early as the 1950's. Recall the definition of a Toeplitz operator from We say that the differential operator T is of the main original motivations for its development. currently being used to classify phases of matter!). the first section. We are now in a position to state elliptic if whenever 1 d) ≠ 0, the linear THEOREM (Raoul Bott, 1958) For a more detailed discussion of these ideas, the A point e in the fiber E over x of the vector bundle our first index theorem, describing the index of a x transformation T (x, 𝜉 : E ⟶ Fx is invertible Suppse 2N n. If n is odd, then each map f as above, reader is referred to [Ati67, Ati68]. The richness of the mathematics underlying the is described by co-ordinates m given by 휉 = (휉 , ... , 휉 Toeplitz matrix in terms of the winding number of E U Examples of elliptic operators include the Laplacian from the (n – 1)-sphere S n–1 to the space GL ( N, ) index theorem is also reflected in the multitude 휎 6 x (e) = (x, (e)), for all x in the neighborhood U. ≥ The index theorem and its applications its symbol: U U acting on functions or differential forms, the Dirac of N × N invertible complex-valued matrices, can be of proofs that have been given for it. The original � ∈ ℂ ℂ The data of the vector bundle E is equivalent to the operator (a 'square root' of the Laplacian, which deformed to a constant map. For n even, there is an We can now state the Atiyah-Singer index theorem: proof [AS63] relied on the cobordism theory of THEOREM (Toeplitz index theorem) 휓 휃 Δ data of transition functions gUV (x), taking values in plays an important role in quantum mechanics), and integer deg ( f ) associated with any such map f, such manifolds. Soon after that, Atiyah and Singer gave If T is a Toeplitz operator with symbol : S1 THEOREM (Atiyah-Singer, 1963) m × m invertible complex valued matrices, which the operator d + d* acting on differential forms. Here that their K-theoretic proof, which is closest in spirit to σ The analytic index of an elliptic partial differential that is nowhere zero, then T is Fredholm and tell us how to change from the ' coordinate is the exterior derivative. the discussion in this article. Later on, other proofs ⟶ ℂ V d ind (T ) = –deg ( ). – f can be deformed to g if and only if operator on a compact manifold X is equal to the σ system' on Ex to the ' U coordinate system', for were discovered that relied on a study of the heat 휓 Let us further assume that X is compact (it does not topological index of its symbol. The Atiyah-Singer index theorem is formally x U V . deg ( f ) = deg ( g ) equation, the equation that describes the flow of 휓 have punctures or ends that go off to infinity). The analogous to the Toeplitz index theorem, although As an illustration of the power of this theorem, we heat. Yet another argument is based on ideas from If ∈X is ∩a manifold, then an example of a vector relevance of ellipticity is explained by the following – For any integer k there is a map f with deg ( f ) = k. it is much deeper. The role of the Toeplitz operator mention two important mathematical results that quantum field theory. For a detailed discussion of bundle on X is obtained by taking Ex = Tx X, the facts: is played by an elliptic partial differential operator. Just as in the case of the winding number, there are are special cases of the index theorem: all this and more, we refer the reader to the book space of tangent vectors to X at the point x. This Roughly speaking, the symbol of an elliptic partial FACT: If T is elliptic, then it is Fredholm: if U is the many ways of describing and computing deg ( f ), [BB85], and the references therein. is called the tangent bundle, and denoted T X, THE GAUSS-BONNET-CHERN THEOREM differential operator is a higher dimensional space of solutions to T( ) = 0 and U* is the space of drawing on ideas from the different branches of and a section of this bundle is called a vector field. This is a fundamental theorem in differential Conclusion analogue of the Toeplitz symbol, with the S1 being topology. Another example is the bundle k of differential solution to T*( ) = 0, then both U and U* are finite The Atiyah-Singer index theorem reveals × T X 휙 geometry. Suppose a surface is cut into triangles, so replaced by on odd-dimensional sphere, and ∨ dimensional, and so the index of T is well-defined. k-forms on X, which is obtained by taking Ex to be Now suppose we are given an elliptic partial that there are vertices, edges and faces. fundamental connections between analysis, being replaced by the space of invertible N × N 휙 V E F Euler ⋀ ×k ℂ space of multilinear mappings (Tx X ) . differential equation given by a differential operator topology, algebra and physics. Drawing on a diverse matrices. The topological index of the symbol of an Since the index of a Fredholm operator is not observed that the quantity V–E+F is independent sensitive to deformations, it is natural to expect that acting on sections of some vector bundle E and of how we cut the surface into triangles, and and eclectic set of ideas, yet underpinned by simple elliptic differential operator is a higher analogue of If X is equipped with a notion of volume⟶ (e.g.,ℂ if X taking values in the sections of a vector bundle F. Its unifying principles, it draws our attention to the the winding number. the index has an expression in purely topological does not change under continuous deformations is a Riemannian manifold), and the vector spaces Ex underlying unity of mathematics and science. It has terms. This led Israel Gelfand, in 1960, to pose the symbol defines a map (x, 𝜉 : E ⟶ Fx for each x i of the surface. This quantity is called the Euler are equipped with hermitian inner products The index of elliptic partial differential —, — x provided the impetus for cross-fertilization between problem of finding a topological formula for the X and in the tangent space Tx X (for the experts: we characteristic of the surface. The theorem of varying continuously with x, then we can define 휎 7 x equations 〈 〉 index. It is this problem that was solved by Michael have implicitly identified the tangent bundle with the Gauss-Bonnet expresses the Euler characteristic of a subjects and the creation of entire disciplines, 휉 Interesting examples of Fredholm operators cotangent bundle by choosing a Riemannian metric). radically transforming the mathematical landscape 1 , 2 1(x) , 2 (x) x volX Atiyah and Isadore Singer with their proof of the surface as an integral of the curvature of the surface, arise from the study of linear partial differential X index theorem. In other words, the symbol can be viewed as a map thus relating the global topological properties in the process. In all of these respects, it epitomizes equations. Consider a system of linear partial 〈휙 휙 〉 := � 〈휙 휙 〉 The collection of sections for which , is : E F between vector bundles living on the of the surface to local geometric features. The much of Atiyah's work. The deep ideas underlying differential equations on a d-dimensional space X: The topology of the group of invertible � � finite form an infinite dimensional inner product tangent bundle T X. Here E (x, ) = Ex and F (x, ) = Fx. Gauss‑Bonnet‑Chern theorem is a generalization the index theorem will undoubtedly continue to play 휙 2 〈휙 휙 〉 휎 ⟶ � � space (a Hilbert space), denoted L ( X, E ). Given matrices The ellipticity of the equation 휉 is the statement휉 that of this theorem to higher dimensions. It can be an important role in the mathematical explorations st ■ a ( x1, ... , xd ) two vector bundles E and F, of ranks m and n Returning now to topology, there are several this map is invertible away from the locus where = 0. of the 21 century. obtained by applying the Atiyah-Singer index x 1 . 훼. . x d r 훼 ���1 d respectively, an operator conceivable ways in which we might imagine trying theorem to the elliptic operator 훼 휕 훼 � 휙 = 0 to generalize the ideas about the winding number If we choose an embedding of our space X inside휉 References where|훼| � the sum is taken휕 over multi-indices휕 = ( 1, 2 2 n T : L (X,E) L (X,F) to higher dimensions. For instance, we might some standard coordinate space , then we d + d* : L2 odd ( X ) L2 even ( X ) [AS63] M. F. Atiyah and I. M. Singer, The index of ... , ) such that r. We may allow = ( , d i 1 observe that × can be deformed continuously to get an induced embedding of tangent bundles elliptic operators oncompact manifolds, Bull. Amer. m 훼 훼 is a differential operator of⟶ degree r if ℝ ... , m ) to take values in . More generally, we n 2n 2n 2n Here d is the exteriorΩ derivative,⟶ d* Ω its adjoint, and Math. Soc. 69 (1963), 422{433. 훼 �훼 � 휙 휙 S1, and so the winding number is concerned with T X T = S = { }. Using this, may allow to take values in a vector space E that ℂ odd ( X ) the bundle of differential forms of odd x the problemof classifying maps f : S 1 S 1 upto and ideas of Bott and Thom, one can use the data 휙 ℂ ⊂ ℝ ℝ ⊂ ℝ ⋃ ∞ [Ati67] M. F. Atiyah, Algebraic topology and elliptic varies with the point x X. Then we can think of T( ) = a degree. The analytic index is easily shown to be 1 훼 d continuous deformation. One natural analogue of of the symbol : E F to construct a vector x1 . . . xd Ω operators, Comm. PureAppl. Math. 20 (1967). as a map : X E := E such that (x) lies r 훼 ��� ⟶ � � 2n equal to the Euler characteristic, and computing the ∈ x X x 휙 � 훼 휕 훼 휙 this in higher dimensions would be the problem of bundle of a certain rank N on S . Any vector bundle 휎 ⟶ topological index using its differential geometric in Ex. We will further assume∈ that for every point |훼| � 휕 휕 n m on a sphere is trivial over the upper hemisphere 휙 휙 ⟶ � 휙 for all sufficiently differentiable sections , and for classifying continuous maps f : S S between [BB85] B. Booss and D. D. Bleecker, Topology and x in X there is a neighborhood U with such that and over the lower hemisphere, because each of incarnation (see the discussion on winding numbers some matrix valued functions a (strictly speaking, spheres of dimensions n and m, respectively. analysis, Universitext,Springer-Verlag, New York, m 휙 ⟶ above) gives a formula in terms of the curvature of EU := x U Ex is identified withU × via a map This is the problem of determining the these spaces can be deformed to a point. So any 1985, The Atiyah-Singer index formula and gauge- a ( x ) takes values in the vector 훼space Hom ( E , F ) homotopy x x the space. ∈ m such vector bundle is determined by the transition U : EU U × compatible with the projections groups of spheres. This remains one of the deepest theoretic physics, Translated from the German by ∪ ℂ of훼 linear operators from Ex to Fx ; in local function g : S2n–1 GL (N, ) that tells us how the and . to X; we say that E is trivialized over U by U. If E coordinates, such an operator can be represented open problems in mathematics. Its pursuit has UL THE HIRZEBRUCH-RIEMANN-ROCH THEOREM Bleecker A. Mader 휓 ⟶ ℂ coordinates transform on the bundle as we move is equipped with a collection of trivializations as by an × matrix). We require that at least one of brought into existence entire new disciplines within Algebraic geometry is the study of spaces that 휓 n m ⟶ ℂ Pranav Pandit is a mathematician and a faculty topology, and led to the discovery of beautiful from the upper hemisphere to the lower hemisphere. above, we say that E is a vector bundle of rank m on the a with | | = r is not identically zero. arise as solutions to polynomial equations. The 2n–1 member at ICTS-TIFR, Bangalore. new mathematical structures over the last several Here the S is the equator of the 2n-dimensional X, and that is a section of E. 훼 Hirzebruch-Riemann-Roch theorem is a cornerstone 훼 휙 www.icts.res.in www.icts.res.in 8 | ICTS NEWS | VOLUME V | ISSUE 1 2019 9
the motivation to say abstractly what a hyperbolic Thus is a tree with respect to the above structure (since H is a subgroup of G) and the metric space is. Gromov defined a hyperbolic metric generating ΓF2 set. In particular, the Cayley graph geometric structure ( is a subgraph of ). HYPERBOLIC GEOMETRY AND CHAOS IN THE space to be one where triangles are thin or skinny, is hyperbolic. Gromov [Gro85]) defined a finitelyΓF 2 What happens at infinity,ΓH at the boundary?ΓG How i.e. they are tree-like with a bounded amount of generated group do the fractal boundaries interact? We make this error. to be a hyperbolicG group = question precise as follows? COMPLEX PLANE respect to some finite generating set is a hyperbolic Trees give us the skinniest triangles possible and Question 3.1 MAHAN MJ metric space. are examples of 0−hyperbolic geodesic metric Does i extend to a continuous map between the spaces. We now introduce the next player in the The basic fact that makes the theory take off is fractal boundaries and ? game: symmetries. The mathematical structure we that if a group is hyperbolic with respect to some The answer to the above question is ‘No’ in this Hyperbolic Geometry in Nature Note also that the branches become shorter and food. Hence it is trying to divide/replicate itself as ∂H ∂G shall be using to formalize symmetries will be the generality and a counterexample was found recently Perhaps the quickest way to introduce hyperbolic shorter and finally converge to a dust, which has a fast as possible. The brain too is trying to develop finite generating set, it is hyperbolic with respect notion of discrete groups. Imagine finitely many by Baker and Riley [BR13]. But an analogous geometry is to say that it is the geometry self-similar structure at all scales. Such self-similar fast neuronal connections and hence trying to to any finite generating set. Thus hyperbolicity is a symmetries of a space and all their permutations (and much more classical) problem arises when a underlying trees. Here is a picture of a tree with the objects are called fractals. The specific structure at solve a ‘maximization of surface area’ problem. property of the group, not the particular generating and combinations. Then the collection of all the hyperbolic group acts by symmetries (isometries) foliage removed to expose the underlying structure. the boundary of the tree is called a Cantor set and Whenever there is such an instance of trying to set we choose to construct its Cayley graph. resulting symmetries is called a group and the on , the 3 dimensionalG hyperbolic space given by (Somewhat unkindly to the tree, the geometer is one of the simplest fractals that we can think of. maximize the area of the boundary inside Euclidean Any such hyperbolic group has a boundary, just 3 finitely many we started with are called generators. H equipped with metric. The treats foliage only as clutter.) It is 0-dimensional, in the sense that its connected space, hyperbolic geometry becomes the natural as the boundary of a tree is a Cantor set. Further, 3 There might be relations between the generators, Hboundary = {(x, ofy, z) :is z > 0} , i.e. it is the complex components are points. Thus we see that when we geometry of the object. And a tell-tale signature is boundaries of hyperbolic groups have a natural 3 too. This gives rise to a formal description plane (plus a HpointC at ∪ infinity). {∞} try to force the hyperbolic geometry of a tree into a fractal of one lower dimension at the boundary. fractal structure, which is largely independent of the flat Euclidean space, a fractal in one dimension less The reader is probably familiar with the opposite generating set. The group of (orientation-preserving) isometries naturally arises at its boundary. problem of trying to minimize surface area where G =
www.icts.res.in www.icts.res.in 10 | ICTS NEWS | VOLUME V | ISSUE 1 2019 11
IN S S ICTS RAMANUJAN do not alway exist. Forum of Mathematics, Sigma, LECTURE SERIES of NCRA-TIFR, Pune) Infosys - ICTS Srinivasa Ramanujan Lecture Series are delivered by eminent mathematicians and scientists on important developments in their areas of speciality. The first lecture in any series is aimed at a general audience, while the ALGEBRAIC AND remaining are targeted at specialists. PROGRAMS LECTURES 1, e3, 2013. The Myriad ANALYTIC ASPECTS OF SOME OPEN QUESTIONS VISHVESHWARA LECTURES Colorful Ways AUTOMORPHIC FORMS ABOUT SCALING LIMITS of IN PROBABILITY THEORY The Myriad Colorful Ways of Understanding INFOSYS—ICTS CHANDRASEKHAR LECTURE 1 | Yang-Mills for mathematicians [Gro85] M. Gromov. Hyperbolic Groups. in Essays 4 PM, 14 JANUARY 2019 Understanding Making sense of quantum field theories is one of the most important open problems of modern mathematics. It is not very well known in the mathematics community that many Observing the Birth of the Universe small parts of this big problem are in fact well-posed questions in probability theory. In this talk I will describe a number of probabilistic open questions, which, if solved, would contribute Extreme QCD Matter LECTURE SERIES Extreme QCD 𝑖𝑖 greatly towards the goal of rigorous construction of quantum field theories. Specifically, I will
KQED Science Science KQED Photo: discuss Yang-Mills theories, lattice gauge theories, quark confinement, mass gap and in Group Theory, ed. Gersten, MSRI Publ.,vol.8, PROBABILISTIC METHODS IN gauge-string duality, all as problems in probability. Matter LECTURE 2 | ✦ Preparatory School on Gauge-string duality in lattice gauge theories 1—17 April 2019 ✦ Organizers — 22 January 2019 Speaker — Lyman Page (James 4 PM, 16 JANUARY 2019 NEGATIVE CURVATURE Quantum gauge theories are the mathematically ill-defined building blocks of the The goal of this program is to train the younger researchers comprehensively Standard Model of quantum mechanics. String theories, on the other hand, were built to X-Ray and Microwave Cosmology for confronting this challenge via assimilation of diverse theoretical All applicants are requested to fill in the application form. POPULATION GENETICS The main theme of the program is algebraic and analytic serve as models of quantum gravity. Physicists have long been aware of the existence of a perspectives including lattice gauge theory, perturbative QCD, and also The focal area of the program lies at the juncture of 1) Dmitry Dolgopyat (University of Maryland) aspects of automorphic forms. Applicants should also ask their instructor to fill up the duality between quantum Yang-Mills theories and string theories. This is sometimes Springer Verlag, pages 75–263, 1985. holographic and kinetic approaches for far-from-equilibrium phenomena. called “gauge-string duality” or “gauge-gravity duality”. Making sense of the duality recommendation form. For more details on the application three areas – Circle rotations and dynamics on the modular surface formulas is still well beyond the reach of rigorous mathematics, partly because the models The program comprises of a workshop followed by a procedure visit the program webpage. AND EVOLUTION S. McDonnell Distinguished University Professor in in question have not yet been rigorously defined. In this talk I will present a rigorously The main lectures will be on ❆ Probability theory of random 2) Sebastien Gouezel (University of Nantes) discussion meeting. The aim of the discussion meeting is Speakers in the Workshop proved version of gauge-string duality in a discrete setting. Specifically, I will take a lattice SOURAV Ayan Mukhopadhyay, Sayantan Sharma ๛ Perturbative QCD and effective theories like SCET Random walks on hyperbolic groups - II to bring together mathematicians working in different gauge theory, which is a discrete approximation of a quantum gauge theory, and prove an ✦ walks 17 January 2019 Speaker — Lattice Gauge Theory aspects of automorphic forms, and to discuss the latest Anna von Pippich explicit duality with a kind of string theory on the lattice. The duality has the appearance Rashid Sunyaev ๛ 1. (TU Darmstadt, Germany) Organisers The 2019 preparatory school on Population Genetics and 3) Peter Haissinsky (Aix-Marseille University) of a natural discrete analog of the formulas conjectured for the continuum models. The ๛ Thermal Field theory and hard-thermal-loop resummations in QCD ❆ Ergodic theory of flows on developments in the field. “Theory of Eisenstein series” Deepa Agashe and Kavita Jain Evolution (PGE2019) will be an intensive one-week course question of proving a continuum version of this duality remains open. These and other ๛ Low-x physics Random walks on hyperbolic groups - I designed for students who are interested in population CHATTERJEE open questions will be discussed. (Partly based on joint work with Jafar Jafarov.) Holographic approaches to QCD matter negatively curved spaces The aim of the workshop is to acquaint graduate students 2. Ameya Pitale (University of Oklahoma, USA) ๛ popgen2019 @icts.res.in genetics and evolution. We will cover (1) key mathematical 4) Vadim Kaimanovich (University of Ottawa) and young researchers with the latest developments in “Siegel modular forms: Classical and adelic aspects” Sourav Chatterjee is a Professor of Mathematics and Statistics at Physics, Princeton University) ๛ QCD kinetic theory ❆ Gromov hyperbolic groups Organisers Poisson boundaries www.icts.res.in/program/popgen2019 concepts and tools that would benefit students from a biology LECTURE 3 | Stanford University and one of the leading figures in ๛ Jets in QGP the field. The workshop comprises of four courses, two Constructing a solution of the 2D KPZ and Vincent Sécherre contemporary probability. Chatterjee has made fundamental Ravindran V. 3. (Université de Versailles, France) background, and (2) important concepts and basic knowledge Ayan Mukhopadhyay, Sayantan Sharma & Ravindran V each on the latest developments in the algebraic and 5) Jean-Francois Quint (Institute of Mathematics of “ℓ-Modular representations of p-adic groups” contributions in a broad range of topics, bringing new (Space Research Institute of the Russian Academy [Min02] Y. N. Minsky. The Classification of Kleinian of biology and genetics that would benefit students from a equation Speakers include The program will have 6 mini-courses of 4 lectures analytic aspects of automorphic forms. perspectives to many classical problems in probability theory Bordeaux) [email protected] Random walks on reductive groups Application deadline non-biology background. Rajeev Bhalerao (IISER Pune) each, with each lecture about 1 hour 15 minutes. 4. Shunsuke Yamana (Kyoto University, Japan) 2 PM, 18 JANUARY 2019 and mathematical physics. He is well known for his work on The Kardar-Parisi-Zhang (KPZ) equation has become accepted as the canonical model for www.icts.res.in/program/extremeqandg2019 Johanna Erdmenger (University of Würzburg) 6) Omri Sarig (Weizmann Institute of Science) Selected outstation participants will be provided local “L-functions and theta correspondence for classical groups” Stein's method for normal approximation, non-linear large 15 November 2018 the growth of random surfaces. While the 1D KPZ equation has now deviations and large deviations in random graphs, spin glass Michal Heller (MPI Potsdam) hospitality including accommodation. Limited travel funds We invite applications from postdocs, PhD students and final Symbolic dynamics in negative curvature and applications a vast amount of rigorous mathematical work behind it, the physically important case of theory, lattice gauge theories among many others. are available for domestic travel. The speakers in the Discussion meeting will be year Master’s students from any science background, who Edmond Iancu (IPhT, Saclay) 2D surfaces has remained mathematically intractable. I will describe a first step towards Application deadline Aleksi Kurkela (University of Stavanger/CERN) updated later on the website. want to work on problems in population genetics and constructing a solution of the 2D KPZ equation, by showing the existence of certain Sourav Chatterjee (born in Kolkata, 1979) received his Bachelor Peter Petreczky (BNL) evolution. We will invite a subset of students from the subsequential scaling limits if the parameters of the equation are renormalized in a and Master of Statistics from Indian Statistical Institute, Kolkata, of Sciences, Moscow; Max-Planck Institute of surface groups I: Models and bounds. Ann. of Math. 31 December 2018 Giuseppe Policastro (ENS, Paris) Deadline for sending applications 04–10 FEB 2019 preparatory school to join the next ICTS School on Population suitable way. Many open questions remain, and these will be discussed. (Based on recent and Ph.D. from Stanford University in 2005, advised by Persi joint work with Alex Dunlap.) Diaconis. . Sourav Chatterjee has held faculty positions at EINSTEIN LECTURE Anton Rebhan (TU Wien) 11–22 Genetics and Evolution scheduled in January 2020. ORGANISERS University of California, Berkeley and Courant Institute of Soeren Schlichting (University of Bielefeld) 15 NOVEMBER 2018 Workshop Probabilistic Methods in Negative Curvature Anilatmaja Aryasomayajula (IISER Tirupati) Mathematical Sciences before returning to Stanford as a Michael Spira (PSI, Villigen) RAMANUJAN HALL, Professor in 2013. Chatterjee's work has been recognized with MARCH 2019 25 Feb – 1 Mar, 2019 Venketasubramanian C G (IISER Tirupati) 1 — 17 APRIL 2019 Raju Venugopalan (BNL) www.icts.res.in/program/pmnc2019 many major awards and honours including Rollo Davidson Prize Jurg Kramer (Humboldt-Universität Berlin) (2010), the inaugural Doeblin Prize (2012) and Loève Prize (2013). Venue [email protected] Discussion meeting 171 (2010), 1–107. Dipendra Prasad (TIFR Mumbai) ICTS, BANGALORE 14 – 18 JANUARY 2019 Chatterjee was an invited speaker at ICM 2014 and became an Astrophysics, Garching; Institute for Advanced Study, We will also have talks on special emerging topics like hydrodynamic RAMANUJAN HALL, Anna von Pippich (TU Darmstadt) elected fellow of Institute of Mathematical Statistics in 2018. attractors, novel hybrid approaches, phenomenological methods, neutron Madhava Hall, Organizers 4 – 7 Mar, 2019 Dawn of new astronomy: How Einstein can Anandavardhanan U K (IIT Bombay) MADHAVA HALL, This lecture is part of the program Universality in random ✦ stars and QCD, and a discussion session on collectivity in small systems. ICTS, Bangalore Riddhipratim Basu, Anish Ghosh, Mahan Mj 11—22 March 2019 Organizers — Riddhipratim ICTS, BENGALURU Madhava Hall, ICTS, Bengaluru structures: Interfaces, Matrices, Sandpiles. www.icts.res.in/program/aforms2019 This school is primarily aimed at young doctoral and postdoctoral ICTS,[email protected] BENGALURU researchers. The eligibility criterion for application is simply being Applications deadline www.icts.res.in/lectures/probability-theory involved in research in the areas related to the themes of the school. [email protected] Princeton) IN S S ICTS We encourage applications from all nationalities. 15 October, 2018 CHANDRASEKHAR take from Planck to Hubble LECTURE SERIES Basu, Anish Ghosh and Mahan Mj Subrahmanyan Chandrasekhar Lecture Series are delivered by eminent [Mj14a] M. Mj. Cannon-Thurston Maps for Surface physicists on important new developments in their areas of speciality. The first lecture in any series is aimed at a general scientific audience, while the remaining are targeted at specialists. + ✦ UNIVERSALITY IN LECTURE 1 02 March 2019 Speaker — B. S. Sathyaprakash 5 PM, 17 JANUARY 2019 Groups. Ann. of Math., 179(1), pages 1–80, 2014. x x x AIR-SEA INTERACTIONS IN RANDOM STRUCTURES X-RAY AND MICROWAVE INFOSYS—ICTS RAMANUJAN LECTURE INTERFACES, MATRICES, SANDPILES COSMOLOGY: SYNERGY AND Algebraic and Analytic Aspects of THE BAY OF BENGAL FROM COMPETITION (Pennsylvania State University and Cardiff University) + + + + + + What do we expect from the next MONSOONS TO MIXING The primary focus of this program will be on the theme Speakers include SERIES of universality in the following three different classes of Anirban Basak Rahul Pandit generation X-ray and microwave discrete random structures – Charles Bordenave Leandro Pimentel Punyabrata Pradhan Automorphic Forms (1) Randomly growing interfaces and (1+1) dimensional Arijit Chakraborty telescopes? Organiserss Although total rainfall during the South Asian Monsoon ✦ Mustazee Rahman Venue — National College, Basavanagudi, [Mj14b] M. Mj. Ending Laminations and Cannon- polymer models Sakuntala Chatterjee Eric D'Asaro, Rama Govindarajan, Manikandan Mathur, varies by only ~10% across India, spatiotemporal variability in TBC Debasis Sengupta, Emily Shroyer, Jai Sukhatme and precipitation is large, difficult to predict, and has far-reaching (2) Eigenvalues of random matrices and other point Sourav Chatterjee Daniel Remenik LECTURE 2 TBC Amit Tandon implications for local communities. The dependence of an processes Sunil Chhita Leonardo Rolla 4:30 PM, 18 JANUARY 2019 X1 X2 X3 1 agrarian economy on rainfall makes prediction of monsoon (3) Sandpile models and other Laplacian growth models Ivan CorwinTBC Wioletta Ruszel RASHID TBC Some Open Questions about Scaling Limits in variability of paramount importance to India and other PHYSICS OF THE RADIATION [email protected] Deepak Dhar Tridib Sadhu 25 February—7March 2019 ✦ Organizers — www.icts.res.in/discussion-meeting/ommbob2019 countries in South Asia. Currently, representation of the Mini-course Speakers Patrik Ferrari Tomohiro Sasamoto COSMOLOGY - TBC monsoon in global climate models exhibits large biases over SPECTRA FORMATION DUE TO Bengaluru Thurston Maps, with an appendix by S. Das and M. Charles Bordenave (Université de Toulouse) Shirshendu Ganguly Sunder Sethuraman SUNYAEV the Indian Ocean. In particular, skill in prediction of Subhroshekhar Ghosh Vladas Sidoravicius Workshop on Tomohiro Sasamoto (Chiba University) Sunyaev was the Director (1996-2017) and is now THOMSON SCATTERING OF LOW intraseasonal oscillations (ISOs), which are associated with TBC Participation is by Alan Hammond Allan Sly active (wet) and break (dry) periods, is modest compared to its Daniel RemenikTBC (Univesidad de Chile) Director-Emeritus of the Max-Planck Institute for TBC FREQUENCY PHOTONS ON HOT invitation only Christopher Hoffman Alexander Sodin Astrophysics, Garching. He is a Chief Scientist in the potential, giving reason to strive for improved forecast Probability Theory THE NEXT DECADE Lionel Levine (Cornell University) Herbert Spohn capabilities. Ocean-atmosphere coupled models have greater Pierre Le Doussal Space Research Institute (IKI) of the Russian Academy of Clusters BAO LENSING 21 cm CMB Algebraic Complexity MAXWELLIAN ELECTRONS. Anilatmaja Aryasomayajula, Venketasubramanian skill in representing ISOs compared to stand-alone Lionel Levine Rajat Subhra Hazra Sciences and Maureen and John Hendricks visiting Mj. Geom. Funct. Anal. 24, pages 297–321, 2014. The program also includes Infosys-ICTS Srinivasa Ofer Zeitouni atmospheric models. This discrepancy highlights the S.S. Manna professor of the Institute for Advanced Study, Princeton. Why the spectra formed in the infinite Ramanujan lecture series by Sourav Chatterjee TBC TBC LECTURERS importance of air-sea interaction to ISO prediction. James Martin Paul Zinn Justin He was a PI of the Soviet orbital observatories GRANAT Theory 18–23 FEB 2019 (Stanford University) TBC - TO BE CONFIRMED and Roentgen on the KVANT module of the MIR space expanding Universe differ strongly 3 - 25 Raul Angulo The focus of this workshop is on air-sea interaction within station and Co-PI of the High-Frequency Instrument of 14-18 January 2019 ✦ Speaker — Somnath Bharadwaj Sourav Chatterjee Searching for Einstein's Biggest Blunder RAMANUJAN HALL, the Bay of Bengal, a region that connects the the Planck Spacecraft. At present, he is leading Russian from the spectra observed from J Richard Bond Organisers Algebraic complexity aims at understanding the Organisers JANUARY 2019 ocean-atmosphere-land through processes that regulate scientists in the Spectrum-X project for the two grazing CG, Jurg Kramer, Dipendra Prasad, Prahladh Harsha, Ramprasad Saptharishi and computational aspects of algebraic objects such as Arvind Ayyer, Riddhipratim Basu, Manjunath Krishnapur accretion disks around black holes? Stefano Borgani delivery of freshwater to the nations around its periphery. incidence X-Ray telescopes eROSITA and ART-XC, a joint Srikanth Srinivasan multivariate polynomials, tensors etc. The primary focus in Jens Chluba ICTS, BANGALORE Better characterizations of the structure and processes in the Russia-German mission with a goal to perform a deep this field has been the study of multivariate polynomials, and urs2019 @icts.res.in Bay of Bengal are needed to improve the representation of its all-sky survey. Two of Sunyaev's most famous LECTURE 3 Paolo Creminelli [email protected] its hardness based on the number of addition/multiplication ICTS Bangalore role in the monsoons. www.icts.res.in/program/urs2019 contributions, bearing his name, are the Shakura-Sunyaev 5 PM, 23 JANUARY 2019 Steen Hannestad www.icts.res.in/program/wact2019 operations required to compute it (i.e. via `algebraic circuits´). (Stanford University) ✦ [Thu80] W. P. Thurston. The Geometry and School 3 – 19 January, 2019 standard theory of the disk accretion and 27 January 2019 Speaker — Subhabrata Alan Heavens Over the last 7-8 years, there has been tremendous progress in TWO IMPORTANT MILESTONES IN Workshop 22 – 25 January, 2019 Sunyaev-Zeldovich effect distortion of the CMB. He has Anandavardhanan UK and Anna von Pippich Bhuvnesh Jain Application deadline understanding the questions about about multivariate Application deadline been the Corresponding member of USSR Academy of Roy Maartens polynomial for natural subclasses of circuits, the deep Sciences (1984–1992), Foreign Associate of USA THE HISTORY OF THE UNIVERSE: Organisers relationships between these problems, and also some barrier Samaya Nissanke 25 February 2019 30 September 2018 National Academy of Sciences (1991), Full member of the Rishi Khatri Subha Majumdar Aseem Paranjape results to give clarity on what types of techniques are The last scattering surface and black Lyman Page Russian Academy of Sciences (1992), Member of the Topology of 3-Manifolds. Princeton University promising approaches to the general problems. This five day German National Academy of Sciences “Leopoldina” body photosphere of the Universe. (TIFR, Mumbai) ✦ Venue — IIT Guwahati John Peacock Majumdar workshop would have a series of about 25-30 lectures by (2004) and the Foreign Member of the Royal Society [email protected] Dmitri Pogosyan 25 — 29 MARCH 2019 various researchers in the field comprising of some of the (London) (2009). His awards and honours include the www.icts.res.in/program/cosmo2019 Jonathan Pritchard recent advances in the field and also some tutorials aimed at 14 JAN – 8 FEB 2019 Gold Medal of the Royal Astronomical Society (1995), 17, 18, 23 JANUARY 2019 Varun Sahni Madhava vHall, giving students a gentle introduction to the area. Catherine Bruce Gold Medal (2000), Gruber Cosmology INFOSYS—ICTS DISTINGUISHED Ravi Sheth Prize (2003), Crafoord Prize in Astronomy (2008), Karl Accommodation for outstation/non-local participants will Preparatory School on Population Genetics TBC MADHAVA HALL, Schwarzschild Medal, German Astronomical Society RAMANUJAN HALL, Notes, 1980. David Spergel be provided at our on campus ICTS guest house. Last date of application ICTS, Bengaluru (2008), Kyoto Prize (2011), Benjamin Franklin Medal in 1 SEPTEMBER 2018 Kandaswamy Subramanian Physics (2012), Einstein Professorship of the Chinese ICTS, BENGALURU Rashid Sunyaev ICTS, BANGALORE Academy of Sciences (2014), Yakov Zeldovich Gold Medal Benjamin Wandelt of Russian Academy of Sciences (2015) and the State [email protected] icts.res.in/lectures/microwave-cosmology2019 LECTURE Is the universe geometric or algebraic? Prize of Russia for Science and Technology (2017). An artist's rendering showing the universe's rst, massive, blue stars embedded in gaseous laments, with the cosmic microwave background Underwater (2004 - 2005) - Manuel Caeiro (1975) | Photograph downloaded from flickr.com/photos/pedrosimoes7 | CC BY 2.0 Deepak Sadhu, BG Image courtesy Dhar - Tridib just visible at the edges. Credit: N.R.Fuller, National Science Foundation | https://phys.org/news/2018-02-secrets-universe.html and Evolution ICTS DISTINGUISHED LECTURES ICTS DISTINGUISHED LECTURE In November 1915, Albert Einstein proposed ICTS DISTINGUISHED LECTURE In November 1915, Albert Einstein proposedthe General Theory of Relativity, which General Theory of Relativity THREE LECTURES ON the , which ✦ [Thu82] W. P. Thurston. Three dimensional revolutionized our understanding of gravity revolutionized our understanding of gravity 21 December 2018 Speaker — Minhyong Kim and became one of the pillars of modern and became one of the pillars of modern Topological Quantum physics. ICTS plans to organize a public ✦ lecture series, called “Einstein Lectures,” physics. ICTS plans to organize a public A Golden Age in 4—10 February 2019 Organizers — Deepa A Golden Age in Physics: Heavy Ion Physics at celebrating the centenary year of General lecture series, called “Einstein Lectures,” MACHINE LEARNING Relativity. Educational institutions and other public organizations from all over celebrating the centenary year of General India are invited to partner with ICTS in Relativity. Educational institutions and Matter, Entanglement, organizing public lectures at various venues Physics: in India. ICTS is in the process of assemblingother public organizations from all over 11:30 am, 12 February 2019 Einstein a vibrant pool of Einstein speakers India are invited to partner with ICTS in LECTURE 1 spanning a wide spectrum, ranging from early-career scientists to international organizing public lectures at various venues luminaries. Einstein lectures will carry the ✦ manifolds, Kleinian groups and hyperbolic message of Einstein’s triumphant theory in India. ICTS is in the process of assembling Heavy Ion Physics at Mathematics of Machine and a "Second (University of Oxford, UK and KIAS, South Korea) lectures and its impact on modern physics andGolden a vibrant poolJubilee of Einstein Lectures speakers astronomy, and the spirit of discovery and EinsteinPUBLIC LECTURE SERIES CELEBRATING THE CENTENARY OF LECTURE SERIES ORGANISED BY THE DEANERY OF SCIENCES CELEBRATING scientific temper. spanning a wide spectrum, ranging from Agashe and Kavita Jain High Energies ALBERT EINSTEIN’S GENERAL THEORY OF RELATIVITY THE GOLDEN JUBILEEearly-career OF CHRIST(DEEMED scientists to international TO BE UNIVERSITY) Learning: an Introduction The open call for partner organizations, High Energies along with a list of Einstein lecturers and luminaries. Einstein lectures will carry the Quantum Revolution" topics will be published on the ICTS web site in August. Selected partner organizations message of Einstein’s triumphant theory Machine learning is the sub-field of computer science concerned with creating will work with ICTS in selecting an and its impact on modern physics and programs and machines that can improve from experience and interaction. It relies upon lecturesappropriate speaker depending on the date astronomy, and the spirit of discovery and and venue of the lecture, and the nature of I will give a pedagogical introduction to the modern mathematical optimization, statistics, and algorithm design. The talk will be an the audience. ICTS will provide the necessaryscientific temper. 10 APRIL, 2019 While the laws of quantum mechanics have remained support to organize the event, and the theory of nuclear forces, Quantum Chromo Dynamics introduction to machine learning for a mathematical audience. We describe the geometry. Bull. Amer. Math. Soc., pages 357–382, partner organizations are expected to take Venue — Christ University, Bengaluru unchanged and have passed all tests for the last eighty-five 11 JANUARY, 2019 care of the local organization. The open call for partner organizations, mathematical formulations of basic types of learning such as supervised, unsupervised, ✦ (QCD), a theory of quarks and gluons. I will also discuss 5:00 pm — 6:00 pm 10 April 2019 Speaker — along with a list of Einstein lecturers and interactive, etc., and the philosophical and scientific issues raised by them. Rob Pisarski http://www.icts.res.in/lecture/einstein years, new discoveries about the exotic states that they allow, Public lecture by topics will be published on the ICTS web site the history and results from the collisions of heavy “entanglement”, and ideas from quantum information theory, in August. Selected partner organizations 4:30 pm will work with ICTS in selecting an ions at ultra relativistic energies, which appears to RAMANUJAN HALL, 3 pm, 12 February 2019 have greatly changed our perspective, and some believe that a Minhyong Kim appropriate speaker depending on the date have created a new phase of matter, a Quark-Gluon LECTURE 2 “second quantum revolution” is currently underway. and venue of the lecture, and the nature of ICTS, BENGALURU Universality in Random Structures: Interfaces, the audience. ICTS will provide the necessary Plasma. There is a wealth of experimental results, Toward Theoretical The discovery of unexpected “topological states of matter”, and 1982. University of Oxford, UK and KIAS, South Korea support to organize the event, and the RAMANUJAN HALL, their possible use for “topologically-protected quantum partner organizations are expected to take whose details remain a puzzle to theory. (Brookhaven National Laboratory, USA) care of the local organization. [email protected] Understanding of Deep information processing” is one of the important themes of these developments, and will be described. ICTS, BENGALURU Is the universe http://www.icts.res.in/lecture/einstein www.icts.res.in/lectures/goldenage2019 Learning KAAPI WITH KURIOSITY [email protected] The empirical success of deep learning drives much of the excitement about machine Matrices, Sandpiles learning today. This success vastly outstrips our mathematical understanding. This www.icts.res.in/lectures/quantumrevolution2019 geometric or algebraic? Rob Pisarski lecture surveys progress in recent years toward developing a theory of deep learning. SANJEEV Works have started addressing issues such as speed of optimization, sample In recent years, I have heard distinguished physicists ask this (Brookhaven National Laboratory) requirements for training, effect of architecture choices, and properties of deep Duncan Haldane generative models. Mahan Mj is a mathematician and a faculty member question with increasing frequency and urgency. In this (Sherman Fairchild University Professor A few examples how the science of complex lecture, I will try to convey to the audience some sense of Rob Pisarski is a quantum field theorist, best known ARORA ✦ Three Lectures on Machine Learning the meaning of this question, and present a few simple 4 January—8 February 2019 Organizers — 11:30 am, 13 February 2019 Arvind for his work on gauge theories, especially the reflections on it from the point of view of a mathematician. LECTURE 3 of Physics, Princeton University and development of Hard Thermal Loops semi-classical Princeton University and Minhyong Kim grew up in Seoul, Korea, Theoretical Analysis of Nobel Prize in Physics 2016) and started his study of mathematics at theory of QCD at high temperatures. Recently he IAS, Princeton Seoul National University. After receiving his has been working on effective theories in a partially Unsupervised Learning at the Tata Institute of Fundamental Research, Ph.D. at Yale University, he has taught at systems changes our view of the world confined phase (the semi-Quark Gluon Plasma) and 21 December 2018 (Friday) at 3 pm Sanjeev Arora is Charles C. Fitzmorris Professor of Unsupervised learning refers to learning without human-labeled datapoints. Frederick Duncan Michael Haldane earned his BA in ✦ numerous institutions on three continents. 12-13 February 2019 Speaker — Sanjeev Arora This can mean many things but in this talk will primarily refer to learning and on the Lifshitz regime. 1973 and Ph.D. in 1978 at the University of Cambridge, Ayyer, Riddhipratim Basu Manjunath Computer Science at Princeton University and Christ University, Main Auditorium, His recent ideas aim to bring ideas of physics representations (also called embeddings) of complicated data types such as images or Visiting Professor in Mathematics at the Institute UK and is presently the Sherman Fairchild University into number theory. text. Empirically it is possible to learn such representations which have interesting Hosur Road, Bengaluru - 29. Professor of Physics at Princeton University, USA. This lecture is part of the program "The Myriad for Advanced Study. He works on theoretical properties and also lead to better performance when combined with labeled data. This He is currently Professor of Number Theory computer science and theoretical machine talk will survey some attempts to theoretically understand such embeddings and Haldane is a fellow of the Royal Society, the American at the University of Oxford and a Colorful Ways of Understanding Extreme QCD learning. He has received the Packard Fellowship representations, as well as their properties. Many examples are drawn from natural Academy of Arts and Sciences, American Physical ✦ Mumbai. Distinguished Professor at the Korea Matter". language processing. 26 May 2019 Speaker — Stefan Thurner (Medical Society, the Institute of Physics and the American Institute for Advanced Study. (1997), Simons Investigator Award (2012), Gödel (Princeton University and Institute for Advanced Association for the Advancement of Science. Krishnapur Prize (2001 and 2010), ACM Prize in Computing The distinguished lecture is generously supported by Simons Foundation. Haldane has received many prestigious awards (formerly the ACM-Infosys Foundation Award in including the Oliver E. Buckley Prize of the the Computing Sciences) (2012), and the Fulkerson American Physical Society (1993), Dirac Medal Prize in Discrete Math (2012). He is a fellow of the 12 – 13 FEBRUARY 2019 (2012) and shared the 2016 Nobel Prize in Physics American Academy of Arts and Sciences and University of Vienna) ✦ Venue — J. N. Planetarium, " or theoretical disco eries o to ological hase International Centre for Theoretical Sciences member of the National Academy of Science. Study, USA) transitions and to ological hases o atter" with Tata Institute of Fundamental Research RAMANUJAN HALL, Shivakote, Hesaraghatta Hobli, Bangalore 560089 David J. Thouless and J. Michael Kosterlitz Tel 080 4653 6051 E-mail [email protected] ADMISSION FREE. REGISTER ONLINE AT ICTS, BENGALURU https://icts.res.in/lectures/einstein https://bit.ly/el2018dec Cosmology – The Next Decade Registration deadline - February 10, 2019 Bangalore
[email protected] www.icts.res.in/lectures/machinelearning2019 ABDUS SALAM BG Image via www.vpnsrus.com MEMORIAL LECTURES KAAPI WITH KURIOSITY ✦ Abdus Salam is one of the creators of the Standard Model of 3—25 January 2019 Organizers — Rishi Khatri, Quantum Inflation in the Planck Era and Elementary particles. He won the Nobel Prize in 1979 with Sheldon Glashow and Steven Weinberg. Besides his extensive contributions to physics, he created the International Centre for Theoretical Physics in Trieste, Italy, with the mission of promoting science in the developing world. The Abdus Salam Memorial Lectures are delivered by eminent personalities on their area of specialization and are aimed at a general audience. ADITI DE Subha Majumdar and Aseem Paranjape Beyond Symmetry and the Laws of Nature is a professor at the Harish-Chandra Research Institute (HRI), Allahabad. She along with her colleagues co-founded the Quantum Information and Computation group (QIC) at HRI in NETWORKS AND 2009. She was awarded the prestigious Shanti Swaroop 14 April 2019 ✦ Speaker — Umesh Waghmare Bhatnagar Award in 2018.De’s current research focus is on 15 January 2019 ✦ Speaker — J. Richard Bond MYCOBACTERIUM communication and its implementation in the field of quantum physics and the application of concepts in quantum information science, to study many body-systems. She is also interested in TUBERCULOSISTuberculosis has been and remains to be one of deadliest diseases of the mankind. Caused by the bacterium, Mycobacterium tuberculosis, using quantum mechanics to study characterization of resource currently faces the challenge of prevention, early detection and effective ✦ building technologies, and environmental effects on resources (JNCASR, Bengaluru) Venue — J. N. Planetarium, control. Our laboratory has been working in understanding the biology of this organism using various Biophysical and Biochemical methods. One of that are essential for computer building. (CITA, University of Toronto, Canada) our interests has been to study genome-wide protein: protein interactions and then through applications of graph theory, address various questions. We have been able to propose the mechanisms of its mode of entry into DISCUSSION dormancy through a combination of such a study of interactions and Boolean modeling. We have also proposed methods to study differential gene expressions, especially to delineate role of various control factors. Bangalore More recently, by measuring the concentrations of metabolites, we have QUANTUM attempted to understand its adaptation to various environmental conditions. Through these studies, exciting and valuable insights have been obtained. In my lecture, I will try to present the methodologies behind these results. TECHNOLOGIES
| Centers for Disease Control and Prevention | CDC/ James Archer Topological Quantum Matter, Entanglement, The quantum theory of nature, formalized in the first few 2019 Kate Bernier | accessed on blog.usejournal.com 5 May decades of the 20th century, contains elements that are MEETINGS fundamentally different from those required in the classical description of nature. Based on the laws of How fish swim? quantum mechanics, in recent years, several and a ‘Second Quantum Revolution’ BG Tuberculosis Image resistant - Drug SHEKHAR C. discoveries have been reported which can revolutionize the way we think about modern technologies. I will talk MANDE(Director General of the Council of Scientific and about such inventions in the field of communication and Industrial Research (CSIR) and computation. 17 March 2019 ✦ Speaker — Secretary, Department of Scientific and Industrial Workshop on Algebraic Complexity Theory 11 January 2019 ✦ Speaker — Jaywant H. Arakeri Research (DSIR), Govt of India) Duncan Haldane *3 pm, Sunday, 16th June 2019, Anyone Can Understand Quantum Physics: Part Two, The Uncertainty Principle , by Two, Part Can Understand Quantum Physics: Image from Anyone Jawaharlal Nehru Planetarium, Bengaluru * The talk is at 3 pm, not 4 pm as is, usually. 25-29 March 2019 ✦ Organizer — (IISc, Bengaluru) ✦ Venue — J. N. Planetarium, Lyman Page delivers the ICTS Vishveshwara Lecture 4 pm, 30 April 2019 Prahladh (Sherman Fairchild University Professor of Physics, CHANDRASEKHAR AUDITORIUM,
ICTS, BENGALURU Register: bit.ly/kwk2019june
Register online Harsha, Ramprasad Saptharishi and Srikanth Bangalore https://bit.ly/nmt2019 ictstifr ictstifr ICTStalks Princeton University, USA) www.icts.res.in/lectures/nmt2019 K A A P I WITH K URI O S I T Y KAAPI WITH KURIOSITY KAAPI WITH KURIOSITY KAAPI WITH KURIOSITY KAAPI WITH KURIOSITY Srinivasan The Tau of Ramanujan UMESH WAGHMARE STEFAN THURNER Topics in Quantum Chaos (An Infosys Prize François R. Bouchet received a B Tech (with institute silver medal) in Engineering Physics from the IIT, Bombay is a French cosmologist specializing in physical cosmology, including formation of How fish swim (1990) and a PhD in Applied Physics from Yale University (1996). After post-doctoral work at is professor for Science of Complex Systems at the Medical University of Vienna, external large scale structures and the study of the remnant radiation from the Big Bang. His Harvard University, he joined the faculty at JNCASR in 2000. professor at the Santa Fe Institute, senior researcher at IIASA, and president of the Complexity ✦ research combines theoretical and numerical studies with analysis of data from space- Science Hub Vienna. He obtained a PhD in theoretical physics from the Technical University of Monsoon Day 10 February 2019 Speaker — Eknath Ghate (TIFR, Fish and other aquatic animals swim in myriad ways. From the and ground-based telescopes. He is based at the lnstitut d'Astrophysique de Paris, In his research, he uses fundamental principles of Physics to derive interatomic interactions, Vienna and a PhD in economics from the University of Vienna. His research focus is on the Lecture) fast swimming shark where mostly just the tail wags, to the and computer simulations to predict and understand the structure, properties and mechanisms understanding of complex systems. Stefan Thurner has published more than 200 scientific where he has served as overseer of the data analysis effort for the Planck satellite eel where a wave moves down its whole body as it swims mission. Dr. Bouchet is the Head of the CMB/Planck Team at IAP and the Deputy of phase transitions in various materials. He is presently the chief editor of ‘Pramana Journal of articles. His work has been covered extensively by the media, and is featured in more than 500 The Tau of forward, to the sting ray that seems to ‘fly’ through water. Are Physics’ and an associate editor of ‘Nanoscale’. He is also interested in science outreach newspaper, radio and television reports. Principal Investigator of the Planck-HFI consortium. fish more efficient swimmers than man-made underwater activities and mountaineering. vehicles like submarines? Are their wakes ‘quieter’? Can we ✦ ✦ indeed define an efficiency for a self-propelling body moving 24 February 2019 Organizers — Amit Apte, Rama ✦ Mumbai) Venue — J. N. Planetarium, Bangalore Ramanujan at constant speed? Many fish bodies and their fins and tails 3 January 2019 Speaker — Nalini Anantharaman are highly flexible. Is flexibility important? How much flexibility is good? Do skins of aquatic animals have special textures that The sequence of numbers 1, -24, 252, -1472, 4830, ... was extensively studied by the reduce drag? In this talk I will discuss some of these great Indian mathematician Ramanujan almost a century ago. These numbers - the values questions, answers to which are mostly unknown. A FEW EXAMPLES HOW THE of Ramanujan's tau-function - have been the guiding force behind several themes in SYMMETRY AND and Number Theory. They continue to tantalize us with easy-to-understand problems some of Govindarajan Vishal Vasan Our Amazing Universe which are still open today. This talk will be a relaxed introduction to these numbers and SCIENCE OF COMPLEX SYSTEMS (Institute for Advanced Study, USA and University of will lead up to some of our own results about them. Astronomical revelations and new mysteries THE LAWS OF NATURE Principles of symmetry are the most fundamental ingredients of our physical Our amazing Universe: astronomical JAYWANT H. ARAKERI description of nature evolved over the last century: (a) permissible physical laws CHANGES OUR VIEW OF THE WORLD and interactions are constrained by symmetry and involve regularities Jaywant H Arakeri is in the faculty of the Mechanical Engineering department the irrespective of diverse systemic details, (b) spontaneous symmetry breaking Centre for Product Design and Manufacture at the Indian Institute of Science, The science of complex systems is a relatively new field that tries to understand the Strasbourg, France) results in the texture of the world we live in. We illustrate these beautiful ideas Bangalore. All his education has been in aeronautical engineering, BTech (IIT, nature of systems that were until now thought to be too complicated to be accessible to EKNATH GHATE by posing a few curious questions about the things we readily find around us: Madras), ME (IISc) and PhD (Caltech). His research is primarily focused on the (i) Why is the momentum of an object conserved? (ii) Why does a transverse science. These systems include eco-systems, societies, financial markets or cities. is a Professor at the School of Mathematics at the TIFR in Mumbai. His research is in Number fundamental understanding of various phenomena in fluid mechanics. Some of the In combination with big data, for the first time, it becomes possible to understand Air-Sea Interactions in the Bay of Bengal from revelations and new mysteries sound wave exist in a crystal, but not in a liquid? (iii) How does a magnet lose its Theory, a branch of Pure Mathematics. He has a BA in Mathematics, summa cum laude, from questions being addressed in his lab relate to the role of turbulence in condensation magnetic property above Curie temperature? (iv) Why does a magnet not feel relevant properties of such systems, such as their efficiency, their resilience and the University of Pennsylvania, and a Ph D from the University of California, Los Angeles. and droplet growth in clouds; flows around flexible surfaces like fish tails and heart any force in static electric field? and (v) How does the ZnO crystal exhibit robustness. An issue of particular importance is that complex systems collapse. Dr Ghate has taught and lectured on his discoveries at many of the leading universities in the valves; instability of unsteady flows, including those with curvature, like those found piezoelectric property of technological importance whereas MgO does not? A scientific understanding of the nature of collapse can be relevant in understanding US, including Berkeley and Princeton, as well as in Europe, e.g., at the Max Planck Institute in in arteries; heat and moisture loss from soils and leaves. under what conditions systems collapse and how to avoid it. Dr. Bouchet will describe current astronomical observations that Bonn and the University of Paris. He has more than 35 publications, has organised several high level conferences and exchange programs, and serves on several national science ✦ precisely constraint the nature of the Cosmos in which we live, Monsoons to Mixing 20 January 2019 Speaker — François R. Bouchet leading to radical ideas for the origin of the structures within it. This committees and editorial boards. He was awarded one of the the highest awards for inter- ABDUS SALAM MEMORIAL LECTURE touches on questions such as: How did the Universe originate? disciplinary science in India, the Bhatnagar Award, for Mathematical Sciences in 2013. He is a Fellow of the Indian Academy of Sciences. th What is it made of? Why is it the way that it is? What is the nature Sunday, 4 pm, Sunday, 4 pm, 14 April 2019, th th of the mysterious so-called Dark Matter and Dark Energy that Sunday, 4 pm, 17 March 2019, th Jawaharlal Nehru Planetarium, Bengaluru Sunday, 4 pm, 26 May 2019, dominate the composition of the Universe and impose its evolution 20 January 2019, th Jawaharlal Nehru Planetarium, Bengaluru ✦ with time? How do we actually learn about all these? And what are Sunday, 4 pm, 10 February 2019, Jawaharlal Nehru Planetarium, Bengaluru 18—23 February 2019 ✦ Organizers — Eric D'Asaro, (lnstitut d'Astrophysique de Paris, France) Venue — the new mysteries that our observations are revealing? Jawaharlal Nehru Planetarium, Bengaluru Jawaharlal Nehru Planetarium, Bengaluru Nobel laureate Duncan Haldane delivers the ICTS Distinguished Lecture CSH Vienna | shutterstock.com by Image provided Networks and Mycobacterium Tuberculosis Register: bit.ly/kwk2019mar Register: bit.ly/kwk2019feb Register: bit.ly/kwk2019apr Register: bit.ly/kwk2019may Register - bit.ly/kwk2019jan Rama Govindarajan, Manikandan mathur, Debasis J. N. Planetarium, Bangalore ictstifr ictstifr ICTStalks ictstifr ictstifr ICTStalks ictstifr ictstifr ICTStalks ictstifr ictstifr ICTStalks ✦ ictstifr ictstifr ICTStalks 30 April 2019 Speaker — Shekhar C. Mande
ICTS DISTINGUISHED LECTURE Sengupta, Emily Shroyer, Jai Sukhatme and Amit ICTS PUBLIC LECTURE (Director General of the Council of Scientific and Quantum Inflation (UN)SEEN AT LAST: States of Matter in the Planck Era THE BLACK HOLE AND TIFR – CAM, BENGALURU Tandon Indian Statistical Physics and Beyond IN M87 Industrial Research (CSIR) & Secretary, Department How can physicists be so audacious as to declare all we see, hear and The image of a ring of emission at 1.3 mm wavelength at the 9 December 2018 ✦ Speaker — feel is from gravitational instability of quantum fluctuations in 15 JANUARY, 2019 Deepak Dhar Community Meeting 2019 centre of the galaxy M87 has caught everyone’s imagination. It is ultra-early universe fields encoded in energy-density phonons? direct evidence of a long suspected black hole, and was made by Answer: the data reveals it, most precisely by our Planck cosmic combining signals from antennas spanning much of the globe, microwave background (CMB) team. Over the 25 years from the Planck 5:00 pm This lecture will describe three streams flowing into this This is an annual discussion meeting of the Indian statistical physics community attended by scientists, satellite go-ahead to our 2018 Legacy release, we have established the postdoctoral fellows and graduate students, from across the country, working in the broad area of statistical achievement. These are (i) the properties of matter and light physics. SMc, the standard model of cosmology, full of dark energy and matter moving near black holes, (ii) their role in modeling the of Scientific and Industrial Research (DSIR), Govt of amid the subdominant ordinary baryons and leptons. So far our maps of RAMANUJAN HALL, phenomena seen by astronomers at the centres of galaxies, th ✦ the early Universe phonons reveal a two-parameter simplicity, an This meeting will be the 6 in the series and will cover all the 8 topics covered at STATPHYS meetings, namely � and (iii) the techniques and technologies which made possible Indian Statistical Physics Community Meeting (Visiting Faculty, IISER Pune) Venue — J. N. overall amplitude and a nearly scale invariant spectral slope, plus a few an image with angular resolution of 0.1 nano radian, General and mathematical aspects slight anomalies. In the next round of cosmic background and galaxy ICTS, BENGALURU corresponding to a few centimeters at the distance of the Moon. Rigorous results, exact solutions, probability theory, stochastic field theory, phase transitions and critical clustering experiments we are in quest of "Beyond the SMc" physics, phenomena at equilibrium, information theory, optimization, etc. through the emergence of more parameters to characterize the many [email protected] Out-of-equilibrium aspects quantum fields present, including the fundamental gravitons and the Driven systems, transport theory, relaxation and response dynamics, random processes, anomalous diffusion, collective phonon, aka the inflaton. India) fluctuation theorems, large deviations, out-of-equilibrium phase transitions, etc. www.icts.res.in/lectures/plankera2019 RAJARAM ✦ Quantum fluids and condensed matter 14—16 February 2019 Organizers — Ranjini Planetarium, Bangalore Strongly correlated electrons, cold atoms, graphene, mesoscopic quantum phenomena, fractional quantum Hall effect, low dimensional quantum field theory, quantum phase transition s, quantum information, entanglement, Lüttinger liquid, spin liquid, etc. NITYANANDA
Disordered and glassy systems Percolation, spin glasses, structural glasses, metallic glasses, jamming, glass transition, algorithmic problems, etc. J. Richard Bond Rajaram Nityananda currently teaches undergraduate Biological physics physics and mathematics at the Azim Premji University. Molecular motors, single and multicellular dynamics, bacteria, swimmers, spatio-temporal organization, HIs long-standing interest in optics (among other things), biological membranes, biopolymer folding, genomics, biological networks, (CITA, University of Toronto & Canadian nurtured at the National Aerospace laboratory, continued at Bandopadhyay, Abhishek Dhar, Kavita Jain, Rahul evolution models, evolutionary game theory, etc. the Raman Rsearch Institute, and the National Centre for Soft matter Institute for Advanced Research) Radio Astrophysics of the Tata Institute of Fundamental Simple and complex fluids, active matter, molecular and ionic fluids,wetting, self-assembly, polymers, gels, liquid PUBLIC LECTURE Research. This led him into theoretical and computational crystals, microemulsions, foams, membranes, colloids, granular materials, etc. aspects of gravitational lenses, image processing, and radio John Richard "Dick" Bond (OC OOnt FRS FRSC) is a Canadian Life and Motion, One Molecule at a time Nonlinear physics astronomy techniques - all of which have a bearing on the astrophysicist and cosmologist. He served 2 five-year terms Dynamical systems, chaos (classical and quantum), pattern formation, chemical reactions, hydrodynamic subject of this talk. instabilities, turbulence (classical and quantum), etc. 2019 (1996–2006) as CITA's director, is a Senior Fellow in the Canadian Institute for Advanced Research (CIFAR) and served 3 five-year Pandit, Sanjib Sabhapandit, Samriddhi Sankar Interdisciplinary and complex systems Networks and graphs, epidemics, econophysics, social phenomena, traffic flow, ecology, etc. terms (2002-2017) as director of CIFAR's Cosmology and Gravity Program. Bond's most famous works concern the statistics of Recreation of a composition by Piet Mondrian Gaussian random fields in cosmology, the theoretical modeling of 4 pm, 29 April, 2019 ORGANISERS ✦ anisotropies of the cosmic background radiation and quantifying (Un)seen at Last: The Black Hole in M87 18 November 2018 Speaker — (TIFR, Ranjini Bandyopadhyay, Abhishek Dhar, Kavita Jain, Rahul Pandit, Roop Mallik Sanjib Sabhapandit, Samriddhi Sankar Ray, Prerna Sharma the nature of the cosmic web. His very long list of awards include ICTS, Bengaluru the Dannie Heineman Prize for Astrophysics, Officer in the Order of Canada, the Gerhard Herzberg Canada Gold Medal for Science Register online Ray and Prerna Sharma and Engineering, the Killam Award, the Tory Medal, Canadian https://bit.ly/unseenM87 14 – 16 February, 2019 Association of Physicists Medal for Lifetime Achievement in Physics,Queen Elizabeth II Diamond Jubilee Medal, the 2008 ✦ Gruber Prize in Cosmology and as member of the Planck team, 29 April 2019 Speaker — Rajaram Nityananda Mumbai) ✦ Venue — J. N. Planetarium, Bangalore Ramanujan Lecture Hall the 2018 Gruber Prize in Cosmology. ICTS, Bangalore Nalini Anantharaman delivers the Infosys Prize Lecture at ICTS [email protected] www.icts.res.in/discussion-meeting/ispcm2019 (Azim Premji University, Bengaluru & former Director
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