DOCSLIB.ORG

Aaron D. Lauda

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Aaron D. Lauda USCDEPARTMENTOFMATHEMATICS • 3620 S. VERMONT AVE, KAP 108 • LOS ANGELES, CA 90089-2532 E - M A I L:[email protected] • W E B: HTTP://SITES.GOOGLE.COM/VIEW/LAUDA-HOME A A R O N D. L A U D A September 16, 2021 RESEARCH INTERESTS • Low-dimensional topology and topological quantum field theory • Topological quantum computation • Categorification and its applications • Representation theory of Lie algebras and quantum groups EDUCATION 2021 Cambridge University Doctor of Science 2006 Cambridge University Ph.D. Mathematics Thesis: Open-closed topological field theory and Khovanov homology, Advisor: Martin Hyland 2003 University of California, Riverside M.S. in Physics Advisor: John Baez 2002 University of California, Riverside B.S in Pure Mathematics, Summa Cum Laude EMPLOYMENT February 2019 – present University of Southern California, Los Angeles, CA. Dean’s Leadership Fellow for the Natural Sciences and Mathematics March 2014 – present University of Southern California, Los Angeles, CA. Professor November 2013 - March 2014 University of Southern California, Los Angeles, CA. Associate Professor July 2011 - November 2013 University of Southern California, Los Angeles, CA. Assistant Professor Fall 2006– Spring 2011 Columbia University, New York, NY. Joseph Fels Ritt Assistant Professor Fall 2007 Fields Institute, Toronto, Canada. Special Program on ‘Geometric Aspects of Homotopy Theory’ Jerrold E. Marsden Postdoctoral Fellow 1 HONORS AND AWARDS 2021 Doctor of Science, Cambridge University 2019 Fellow of the American Mathematics Society 2016 Mathematical and Physical Sciences Simons Fellow 2014 Section Chair for Seoul ICM Section - Lie Theory and Generalizations 2013 NSF CAREER Award 2011 Alfred P. Sloan Fellowship 2005 Rayleigh-Knight prize, Cambridge University PUBLICATIONS Following the convention in mathematics, authors are listed alphabetically. As mathematicians do not work in labs, their independent research career often begins in graduate school, or sooner. The arXiv numbers correspond to the corresponding entries on the ArXiv preprint server, accessible at http://arxiv.org. Graduate students indicated with (∗) and postdocs with (†). 44. Pseudo-Hermitian Levin-Wen models from non-semisimple TQFTs, with Nathan Geer, Bertrand Patureau- Mirand, and Joshua Sussan, (2021), arXiv:2108.10798. 43. A Hermitian TQFT from a non-semisimple category of quantum sl(2)-modules, with Nathan Geer, Bertrand Patureau-Mirand, and Joshua Sussan, (2021), arXiv:2108.09242. 42. Strands algebras and the affine highest weight property for equivariant hypertoric categories, with Anthony Licata and Andy Manion† (2021), arXiv:2107.06480. 41. Super rewriting theory and nondegeneracy of odd categorified sl(2), with Benjamin Dupont*1 and Mark Ebert* (2021), arXiv:2102.00276. 40. From hypertoric geometry to bordered Floer homology via the m = 1 amplituhedron, with Anthony Licata and Andy Manion† (2020), arXiv:2009.03981. 39. An invitation to categorification, with Joshua Sussan, (2021), To appear in the Notices of American Mathematics Society. 38. Braid group actions from categorical symmetric Howe duality on deformed Webster algebras, with Mikhail Khovanov, Joshua Sussan, Yasuyoshi Yonezawa, To appear in Transformation Groups, (2021), arXiv:1802.05358. 37. Ozsvath-Szabo bordered algebras and subquotients of category O, with Andy Manion† Advances in Mathemat- ics, Volume 376, Issue 6, (2021), arXiv:1910.03770. 36. Curved Rickard complexes and link homologies, with Sabin Cautis and Joshua Sussan, Journal für die reine und angewandte Mathematik (Crelle), Volume 2020, Issue 769, 87–119, (2020), doi.org/10.1515/crelle-2019-0044, arXiv:1901.08195. 35. DG structures on odd categorified quantum sl(2), with Ilknur Egilmez*, Quantum Topology, Volume 11, Issue 2, pp. 227–294, (2020), arXiv:1808.04924. 34. Parameters in categorified quantum groups, Algebras and Representation Theory, Volume 23, pp 1265–1284, (2020), arXiv:1812.07654. 33. The Elliptic Hall algebra and the deformed Khovanov Heisenberg category, with Sabin Cautis, Anthony Licata, Peter Samuelson, Joshua Sussan, Selecta Mathematica, (2018), Volume 24, Issue 5, pp 4041-4103, arXiv:1609.03506. 32. W-algebras from Heisenberg categories, with Sabin Cautis, Anthony M. Licata, Joshua Sussan, Journal of the Institute of Mathematics of Jessieu, Volume 17, Issue 5, November (2018) , pp. 981-101,arXiv:1501.00589. 31. A DG-extention of symmetric functions arising from higher representation theory, with Andrea Appel†, Ilknur Egilmez*, and Matthew Hogancamp†, Journal of Combinatorial Algebra, Vol. 2, (2018), No. 2, 169-214, arXiv:1704.00713. 1Benjamin Dupont was a graduate student at Lyon while collaborating on this project. 2 30. The colored HOMFLYPT function is q-holonomic, with Stavros Garoufalidis and Thang T.Q. Lê, Duke Mathe- matics Journal, Volume 167, Number 3 (2018), 397-447. arXiv:1604.08502. 29. Current algebras and categorified quantum groups, with Anna Beliakova, Kazuo Habiro, and Ben Webster, Journal of the London Mathematical Society, Vol. 95, Issue 1, pages 248–276, (2017), arXiv:1412.1417. 28. Trace decategorification of categorified quantum sl(2), with Anna Beliakova, Kazuo Habiro, and Marko Zivkovic*, Mathematische Annalen, Vol. 367, No.1, (2017) pages 397-440, arXiv:1404.1806. 27. An odd categorification of quantum sl(2), with Alex P. Ellis*, Quantum Topology, Vol. 7, No. 2, (2016), pages 329–433, (2016), arXiv:1307.7816. 26. Cyclicity for categorified quantum groups, with Anna Beliakova, Kazuo Habiro, and Ben Webster, Journal of Algebra, Vol. 452, 118-132, (2016), arXiv:1506.04671. 25. Trace decategorification of the Hecke category, with Ben Elias, Journal of Algebra, Vol. 449, 615-634, (2016), arXiv:1504.05267. 24. Khovanov homology is a skew Howe 2-representation of categorified quantum sl(m), with Hoel Queffelec* and David E. V. Rose†, Algebraic and Geometric Topology, Vol. 15, No. 5, 2515–2606, (2015), arXiv:1212.6076. 23. Implicit structure in 2-representations of quantum groups, with Sabin Cautis, Selecta Mathematica , Volume 21, Issue 1, pp 201-244, (2015), arXiv:1111.1431. 22. Trace as an alternative decategorification functor, with Anna Beliakova, Zaur Guliyev*, and Kazuo Habiro, Acta Mathematica Vietnamica, Volume 39, Issue 4, pp 425-480, (2014), arXiv:1409.1198. 21. Oddification of the cohomology of type A Springer varieties, with Heather Russell†, International Mathematics Research Notices, vol. 2014, No. 17 pages 4822-4854, (2014), arXiv:1203.0797. 20. The odd nilHecke algebra and its diagrammatics, with Alexander Ellis* and Mikhail Khovanov, International Mathematics Research Notices, vol. 2014, No. 4, pages 991–1062, (2014), arXiv:1111.1320. 19. Categorified quantum sl(2) is an inverse limit of flag 2-categories, with Anna Beliakova, Transformation Groups, vol. 19, issue 1, pages 1–26, (2014), arXiv:1205.3608. 18. An introduction to diagrammatic algebra and categorified quantum sl(2), Bulletin of the Institute of Mathematics, Academia Sinica, Taipei, Taiwan, vol. 7, no. 2, pp. 165-270, (2012), arXiv:1106.2128. 17. A categorification of the Casimir of quantum sl(2), with Anna Beliakova and Mikhail Khovanov, Advances in Mathematics, 230, No. 3, pages 1442–1501, (2012) arXiv:1008.0370. 16. Extended graphical calculus for categorified quantum sl(2), with Mikhail Khovanov, Marco Mackaay, and Marko Stoši´c, Memoirs of the AMS, 219, (2012), arXiv:0909.1810. 15. Crystals from categorified quantum groups, with Monica Vazirani, Advances in Mathematics, 228, No. 2, pages 803-861, (2011), arXiv:1006.2866. 14. A diagrammatic approach to categorification of quantum groups II, with Mikhail Khovanov, Transactions of the AMS, 363, pages 2685-2700, (2011), arXiv:0804.2080. 13. Categorified quantum sl(2) and equivariant cohomology of iterated flag varieties, Algebras and Representation Theory, 14, No.2 pages 258-282, (2011), arXiv:0803.3848. 12. A pre-history of n-categorical physics, with John Baez, Deep Beauty: Mathematical Innovation and the Search for an Underlying Intelligibility of the Quantum World, pages 13–128, Cambridge Univ. Press, Cambridge, (2011) arXiv:0908.2469. 11. A categorification of quantum sl(2), Advances in Mathematics, 255, No. 6, pages 3327–3424, (2010), arXiv:0803.3652. 10. Crystals from categorified quantum groups, with Monica Vazirani, Discrete Math. Theor. Comput. Sci. Pro- ceedings, 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010) pp. 869-880. 9. Categorification in Representation Theory with Anthony Licata and Alistair Savage, Editorial in International Journal of Mathematics and Mathematical Sciences (2010), Article ID 592359. 8. Nilpotency in type A cyclotomic quotients, with Alexander Hoffnung, Journal of Algebraic Combinatorics, 32, No. 4 (2010), 533-555, arXiv:0903.2992. 3 7. A diagrammatic approach to categorification of quantum groups III, with Mikhail Khovanov, Quantum Topology 1, No.1, 1–92, (2010) arXiv:0807.3250. 6. A diagrammatic approach to categorification of quantum groups I, with Mikhail Khovanov, Representation The- ory, 3, 309-347, (2009), arXiv:0803.4121. 5. Open-closed TQFTs extend Khovanov homology from links to tangles, with Hendryk Pfeiffer, Journal of Knot Theory and its Ramifications 18, No.1 (2009) 87–150, arXiv:0606331. 4. Open-closed strings: Two-dimensional extended TQFTs and Frobenius algebras, with Hendryk Pfeiffer, Topol- ogy and its Applications 155 (2008), No. 7, 623–666, arXiv:0510664. 3. State sum construction of two-dimensional open-closed Topological Quantum Field Theories, with Hendryk Pfeiffer, Journal of Knot Theory and
Load more

Recommended publications
  • Quantum Topology and Categorification Seminar, Spring 2017
    QUANTUM TOPOLOGY AND CATEGORIFICATION SEMINAR, SPRING 2017 ARUN DEBRAY APRIL 25, 2017 These notes were taken in a learning seminar in Spring 2017. I live-TEXed them using vim, and as such there may be typos; please send questions, comments, complaints, and corrections to [email protected]. Thanks to Michael Ball for finding and fixing a typo. CONTENTS Part 1. Quantum topology: Chern-Simons theory and the Jones polynomial 1 1. The Jones Polynomial: 1/24/171 2. Introduction to quantum field theory: 1/31/174 3. Canonical quantization and Chern-Simons theory: 2/7/177 4. Chern-Simons theory and the Wess-Zumino-Witten model: 2/14/179 5. The Jones polynomial from Chern-Simons theory: 2/21/17 13 6. TQFTs and the Kauffman bracket: 2/28/17 15 7. TQFTs and the Kauffman bracket, II: 3/7/17 17 Part 2. Categorification: Khovanov homology 18 8. Khovanov homology and computations: 3/21/17 18 9. Khovanov homology and low-dimensional topology: 3/28/17 21 10. Khovanov homology for tangles and Frobenius algebras: 4/4/17 23 11. TQFT for tangles: 4/11/17 24 12. The long exact sequence, functoriality, and torsion: 4/18/17 26 13. A transverse link invariant from Khovanov homology: 4/25/17 28 References 30 Part 1. Quantum topology: Chern-Simons theory and the Jones polynomial 1. THE JONES POLYNOMIAL: 1/24/17 Today, Hannah talked about the Jones polynomial, including how she sees it and why she cares about it as a topologist. 1.1. Introduction to knot theory.
    [Show full text]
  • Classical Topology and Quantum States∗
    View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by CERN Document Server SU-4240-716 February 2000 Classical Topology and Quantum States∗ A.P. Balachandran Department of Physics, Syracuse University, Syracuse, NY 13244-1130, USA Abstract Any two infinite-dimensional (separable) Hilbert spaces are unitarily isomorphic. The sets of all their self-adjoint operators are also therefore unitarily equivalent. Thus if all self-adjoint operators can be observed, and if there is no further major axiom in quantum physics than those formulated for example in Dirac’s ‘Quantum Mechanics’, then a quantum physicist would not be able to tell a torus from a hole in the ground. We argue that there are indeed such axioms involving observables with smooth time evolution: they contain commutative subalgebras from which the spatial slice of spacetime with its topology (and with further refinements of the axiom, its CK− and C∞− structures) can be reconstructed using Gel’fand - Naimark theory and its extensions. Classical topology is an attribute of only certain quantum observables for these axioms, the spatial slice emergent from quantum physics getting progressively less differentiable with increasingly higher excitations of energy and eventually altogether ceasing to exist. After formulating these axioms, we apply them to show the possibility of topology change and to discuss quantized fuzzy topologies. Fundamental issues concerning the role of time in quantum physics are also addressed. ∗Talk presented at the Winter Institute on Foundations of Quantum Theory and Quantum Op- tics,S.N.Bose National Centre for Basic Sciences,Calcutta,January 1-13,2000.
    [Show full text]
  • MATTERS of GRAVITY, a Newsletter for the Gravity Community, Number 3
    MATTERS OF GRAVITY Number 3 Spring 1994 Table of Contents Editorial ................................................... ................... 2 Correspondents ................................................... ............ 2 Gravity news: Open Letter to gravitational physicists, Beverly Berger ........................ 3 A Missouri relativist in King Gustav’s Court, Clifford Will .................... 6 Gary Horowitz wins the Xanthopoulos award, Abhay Ashtekar ................ 9 Research briefs: Gamma-ray bursts and their possible cosmological implications, Peter Meszaros 12 Current activity and results in laboratory gravity, Riley Newman ............. 15 Update on representations of quantum gravity, Donald Marolf ................ 19 Ligo project report: December 1993, Rochus E. Vogt ......................... 23 Dark matter or new gravity?, Richard Hammond ............................. 25 Conference Reports: Gravitational waves from coalescing compact binaries, Curt Cutler ........... 28 Mach’s principle: from Newton’s bucket to quantum gravity, Dieter Brill ..... 31 Cornelius Lanczos international centenary conference, David Brown .......... 33 Third Midwest relativity conference, David Garfinkle ......................... 36 arXiv:gr-qc/9402002v1 1 Feb 1994 Editor: Jorge Pullin Center for Gravitational Physics and Geometry The Pennsylvania State University University Park, PA 16802-6300 Fax: (814)863-9608 Phone (814)863-9597 Internet: [email protected] 1 Editorial Well, this newsletter is growing into its third year and third number with a lot of strength. In fact, maybe too much strength. Twelve articles and 37 (!) pages. In this number, apart from the ”traditional” research briefs and conference reports we also bring some news for the community, therefore starting to fulfill the original promise of bringing the gravity/relativity community closer together. As usual I am open to suggestions, criticisms and proposals for articles for the next issue, due September 1st. Many thanks to the authors and the correspondents who made this issue possible.
    [Show full text]
  • Topological Quantum Computation Zhenghan Wang
    Topological Quantum Computation Zhenghan Wang Microsoft Research Station Q, CNSI Bldg Rm 2237, University of California, Santa Barbara, CA 93106-6105, U.S.A. E-mail address: [email protected] 2010 Mathematics Subject Classification. Primary 57-02, 18-02; Secondary 68-02, 81-02 Key words and phrases. Temperley-Lieb category, Jones polynomial, quantum circuit model, modular tensor category, topological quantum field theory, fractional quantum Hall effect, anyonic system, topological phases of matter To my parents, who gave me life. To my teachers, who changed my life. To my family and Station Q, where I belong. Contents Preface xi Acknowledgments xv Chapter 1. Temperley-Lieb-Jones Theories 1 1.1. Generic Temperley-Lieb-Jones algebroids 1 1.2. Jones algebroids 13 1.3. Yang-Lee theory 16 1.4. Unitarity 17 1.5. Ising and Fibonacci theory 19 1.6. Yamada and chromatic polynomials 22 1.7. Yang-Baxter equation 22 Chapter 2. Quantum Circuit Model 25 2.1. Quantum framework 26 2.2. Qubits 27 2.3. n-qubits and computing problems 29 2.4. Universal gate set 29 2.5. Quantum circuit model 31 2.6. Simulating quantum physics 32 Chapter 3. Approximation of the Jones Polynomial 35 3.1. Jones evaluation as a computing problem 35 3.2. FP#P-completeness of Jones evaluation 36 3.3. Quantum approximation 37 3.4. Distribution of Jones evaluations 39 Chapter 4. Ribbon Fusion Categories 41 4.1. Fusion rules and fusion categories 41 4.2. Graphical calculus of RFCs 44 4.3. Unitary fusion categories 48 4.4. Link and 3-manifold invariants 49 4.5.
    [Show full text]
  • Quantum Topology and Quantum Computing by Louis H. Kauffman
    Quantum Topology and Quantum Computing by Louis H. Kauffman Department of Mathematics, Statistics and Computer Science 851 South Morgan Street University of Illinois at Chicago Chicago, Illinois 60607-7045 [email protected] I. Introduction This paper is a quick introduction to key relationships between the theories of knots,links, three-manifold invariants and the structure of quantum mechanics. In section 2 we review the basic ideas and principles of quantum mechanics. Section 3 shows how the idea of a quantum amplitude is applied to the construction of invariants of knots and links. Section 4 explains how the generalisation of the Feynman integral to quantum fields leads to invariants of knots, links and three-manifolds. Section 5 is a discussion of a general categorical approach to these issues. Section 6 is a brief discussion of the relationships of quantum topology to quantum computing. This paper is intended as an introduction that can serve as a springboard for working on the interface between quantum topology and quantum computing. Section 7 summarizes the paper. This paper is a thumbnail sketch of recent developments in low dimensional topology and physics. We recommend that the interested reader consult the references given here for further information, and we apologise to the many authors whose significant work was not mentioned here due to limitations of space and reference. II. A Quick Review of Quantum Mechanics To recall principles of quantum mechanics it is useful to have a quick historical recapitulation. Quantum mechanics really got started when DeBroglie introduced the fantastic notion that matter (such as an electron) is accompanied by a wave that guides its motion and produces interference phenomena just like the waves on the surface of the ocean or the diffraction effects of light going through a small aperture.
    [Show full text]
  • Quantum Gravity: a Primer for Philosophers∗
    Quantum Gravity: A Primer for Philosophers∗ Dean Rickles ‘Quantum Gravity’ does not denote any existing theory: the field of quantum gravity is very much a ‘work in progress’. As you will see in this chapter, there are multiple lines of attack each with the same core goal: to find a theory that unifies, in some sense, general relativity (Einstein’s classical field theory of gravitation) and quantum field theory (the theoretical framework through which we understand the behaviour of particles in non-gravitational fields). Quantum field theory and general relativity seem to be like oil and water, they don’t like to mix—it is fair to say that combining them to produce a theory of quantum gravity constitutes the greatest unresolved puzzle in physics. Our goal in this chapter is to give the reader an impression of what the problem of quantum gravity is; why it is an important problem; the ways that have been suggested to resolve it; and what philosophical issues these approaches, and the problem itself, generate. This review is extremely selective, as it has to be to remain a manageable size: generally, rather than going into great detail in some area, we highlight the key features and the options, in the hope that readers may take up the problem for themselves—however, some of the basic formalism will be introduced so that the reader is able to enter the physics and (what little there is of) the philosophy of physics literature prepared.1 I have also supplied references for those cases where I have omitted some important facts.
    [Show full text]
  • A Rosetta Stone for Quantum Mechanics with an Introduction to Quantum Computation
    Proceedings of Symposia in Applied Mathematics Volume 68, 2010 A Rosetta Stone for Quantum Mechanics with an Introduction to Quantum Computation Samuel J. Lomonaco, Jr. Abstract. The purpose of these lecture notes is to provide readers, who have some mathematical background but little or no exposure to quantum me- chanics and quantum computation, with enough material to begin reading the research literature in quantum computation, quantum cryptography, and quantum information theory. This paper is a written version of the first of eight one hour lectures given in the American Mathematical Society (AMS) Short Course on Quantum Computation held in conjunction with the Annual Meeting of the AMS in Washington, DC, USA in January 2000. Part 1 of the paper is a preamble introducing the reader to the concept of the qubit Part 2 gives an introduction to quantum mechanics covering such topics as Dirac notation, quantum measurement, Heisenberg uncertainty, Schr¨odinger’s equation, density operators, partial trace, multipartite quantum systems, the Heisenberg versus the Schr¨odinger picture, quantum entanglement, EPR para- dox, quantum entropy. Part 3 gives a brief introduction to quantum computation, covering such topics as elementary quantum computing devices, wiring diagrams, the no- cloning theorem, quantum teleportation. Many examples are given to illustrate underlying principles. A table of contents as well as an index are provided for readers who wish to “pick and choose.” Since this paper is intended for a diverse audience, it is written in an informal style at varying levels of difficulty and sophistication, from the very elementary to the more advanced. 2000 Mathematics Subject Classification.
    [Show full text]
  • Quantum Computing and Quantum Topology
    Beyond Anyons: From Fractons to Black Holes Zhenghan Wang Microsoft Station Q & UC Santa Barbara Vanderbilt, May 8, 2019 “Periodic Table” of Topological Phases of Matter Classification of enriched topological order (TQFT) in all dimensions Too hard!!! Special cases: 1): short-range entangled (or symmetry protected--SPT) including topological insulators and topological superconductors: X.-G. Wen et al (group cohomology), …, and A. Ludwig et al (random matrix theory) and A. Kitaev (K-theory)---generalized cohomologies,… 2): Low dimensional: spatial dimensions D=1, 2, 3, n=d=D+1 2a: classify 2D topological orders without symmetry 2b: enrich them with symmetry 2c: 3D much more interesting and harder Model Topological Phases of Quantum Matter Local Hilbert Space Local, Gapped Hamiltonian E Two gapped Hamiltonians 퐻1, 퐻2 realize the same topological phase of matter if there exists a continuous path connecting Egap them without closing the gap/a phase transition. A topological phase, to first approximation, is a class of gapped Hamiltonians that realize the same phase. Topological order in a 2D topological phase is encoded by a TQFT or anyon model. Anyons in Topological Phases of Matter Finite-energy topological quasiparticle excitations=anyons b Quasiparticles a, b, c a c Two quasiparticles have the same topological charge or anyon type if they differ by local operators Anyons in 2+1 dimensions described mathematically by a Unitary Modular Tensor Category Anyonic Objects • Anyons: simple objects in unitary modular categories • Symmetry defects:
    [Show full text]
  • Scientific Workplace· • Mathematical Word Processing • LATEX Typesetting Scientific Word· • Computer Algebra
    Scientific WorkPlace· • Mathematical Word Processing • LATEX Typesetting Scientific Word· • Computer Algebra (-l +lr,:znt:,-1 + 2r) ,..,_' '"""""Ke~r~UrN- r o~ r PooiliorK 1.931'J1 Po6'lf ·1.:1l26!.1 Pod:iDnZ 3.881()2 UfW'IICI(JI)( -2.801~ ""'"""U!NecteoZ l!l!iS'11 v~ 0.7815399 Animated plots ln spherical coordln1tes > To make an anlm.ted plot In spherical coordinates 1. Type an expression In thr.. variables . 2 WMh the Insertion poilt In the expression, choose Plot 3D The next exampfe shows a sphere that grows ftom radius 1 to .. Plot 3D Animated + Spherical The Gold Standard for Mathematical Publishing Scientific WorkPlace and Scientific Word Version 5.5 make writing, sharing, and doing mathematics easier. You compose and edit your documents directly on the screen, without having to think in a programming language. A click of a button allows you to typeset your documents in LAT£X. You choose to print with or without LATEX typesetting, or publish on the web. Scientific WorkPlace and Scientific Word enable both professionals and support staff to produce stunning books and articles. Also, the integrated computer algebra system in Scientific WorkPlace enables you to solve and plot equations, animate 20 and 30 plots, rotate, move, and fly through 3D plots, create 3D implicit plots, and more. MuPAD' Pro MuPAD Pro is an integrated and open mathematical problem­ solving environment for symbolic and numeric computing. Visit our website for details. cK.ichan SOFTWARE , I NC. Visit our website for free trial versions of all our products. www.mackichan.com/notices • Email: info@mac kichan.com • Toll free: 877-724-9673 It@\ A I M S \W ELEGRONIC EDITORIAL BOARD http://www.math.psu.edu/era/ Managing Editors: This electronic-only journal publishes research announcements (up to about 10 Keith Burns journal pages) of significant advances in all branches of mathematics.
    [Show full text]
  • Bohmian Pathways Into Chemistry: a Brief Overview
    Bohmian Pathways into Chemistry: A Brief Overview Angel´ S. Sanz Department of Optics, Faculty of Physical Sciences, Universidad Complutense de Madrid, Pza. Ciencias 1, Ciudad Universitaria 28040 - Madrid, Spain a.s.sanz@fis.ucm.es Perhaps because of the popularity that trajectory-based methodologies have always had in Chemistry and the important role they have played, Bohmian mechanics has been increas- ingly accepted within this community, particularly in those areas of the theoretical chem- istry based on quantum mechanics, e.g., quantum chemistry, chemical physics, or physical chemistry. From a historical perspective, this evolution is remarkably interesting, particu- larly when the scarce applications of Madelung’s former hydrodynamical formulation, dat- ing back to the late 1960s and the 1970s, are compared with the many different applications available at present. As also happens with classical methodologies, Bohmian trajectories are essentially used to described and analyze the evolution of chemical systems, to design and implement new computational propagation techniques, or a combination of both. In the first case, Bohmian trajectories have the advantage that they avoid invoking typical quantum-classical correspondence to interpret the corresponding phenomenon or process, while in the second case quantum-mechanical effects appear by themselves, without the necessity to include artificially quantization conditions. Rather than providing an exhaus- tive revision and analysis of all these applications (excellent monographs on the issue are available in the literature for the interested reader, which can be consulted in the bibliogra- phy here supplied), this Chapter has been prepared in a way that it may serve the reader to acquire a general view (or impression) on how Bohmian mechanics has permeated the different traditional levels or pathways to approach molecular systems in Chemistry: elec- tronic structure, molecular dynamics and statistical mechanics.
    [Show full text]
  • Quantum Topology and Curve Counting Invariants Andrea Brini
    Quantum topology and curve counting invariants Andrea Brini To cite this version: Andrea Brini. Quantum topology and curve counting invariants. 2017. hal-01474196 HAL Id: hal-01474196 https://hal.archives-ouvertes.fr/hal-01474196 Preprint submitted on 22 Feb 2017 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Quantum topology and curve counting invariants Andrea Brini Abstract. Gopakumar, Ooguri and Vafa famously proposed the existence of a correspondence between a topological gauge theory { U(N) Chern{Simons theory on the three-sphere { on one hand, and a topo- logical string theory { the topological A-model on the resolved conifold { on the other. On the physics side, this duality provides a concrete instance of the large N gauge/string correspondence where exact computations can be performed in detail; mathematically, it puts forward a triangle of striking relations between quantum invariants (Reshetikhin{Turaev{Witten) of knots and 3-manifolds, curve-counting invari- ants (Gromov{Witten/Donaldson{Thomas) of local Calabi-Yau 3-folds, and the Eynard{Orantin recursion for a specific class of spectral curves. I here survey recent results on the most general frame of validity of the strongest form of this correspondence and discuss some of its implications.
    [Show full text]
  • The Electromagnetic Origin of Quantization and the Ensuing Changes in Copenhagen Interpretation Ej Post
    Annales Fondation Louis de Broglie, Volume 27, no 2, 2002 217 THE ELECTROMAGNETIC ORIGIN OF QUANTIZATION AND THE ENSUING CHANGES IN COPENHAGEN INTERPRETATION E J POST, 7933 Breen Ave, Westchester, CA 90045-3357; e-mail: [email protected] ABSTRACT. The pre-1925 quantum prescriptions of Planck, Ein- stein, Bohr, Sommerfeld and recently Aharonov-Bohm permit a re- casting as part of a complete set of electromagnetic residue integrals such as used in a mathematical discipline known as de Rham coho- mology. The ensuing spacetime topological reorganization of early quantum aspects seems well supported by Josephson- and quantum Hall effects. This reversal of priorities demands a physical read- justment of standard nonclassical Copenhagen pronouncements. The Schroedinger equation becomes a tool solely applicable to en- sembles consisting of single systems of random phase and - orientation. This reorganization is a return to the ensemble initia- tives of the Thirties by Slater, Popper, Kemble and others, which now can be given a compelling form by identifying long standing classical counter-examples to Copenhagen’s nonclassical proposi- tions. Heisenberg uncertainty and zero-point energy have to yield their pedestal of universal absolute status. They now become mani- festations governing order-disorder transitions in ensembles. key words: quantum topology, Copenhagen, ensemble, single system 1 Introduction This essay aims at new basic perspectives for electromagnetic theory that are contingent on an incisive revision of the Copenhagen interpretation of quantum mechanics. This revision does not affect established mathematical procedures of quantum mechanics. Instead, it addresses a more precise de- 218 E. J. Post lineation of its objects of description and how they relate to reality.
    [Show full text]