Curriculum Vitae ARTAN SHESHMANI

Total Page:16

File Type:pdf, Size:1020Kb

Curriculum Vitae ARTAN SHESHMANI Curriculum Vitae ARTAN SHESHMANI Office Address, Department of Mathematics, Massachusetts Institute of Technology (MIT) Room 2-247 182 Memorial drive, Cambridge, MA, 02139 Office Phone, +1 (614) 565-1659 Homepages, https://people.math.osu.edu/sheshmani.1/Welcome.html http://db.ipmu.jp/member/personal/2970en.html Date of CV, August 2015 Research interests Algebraic Geometry, Enumerative Geometry (Gromov-Witten theory, Donaldson-Thomas theory) Mirror symmetry, Mathematics of String theory Employment 2016 { Visiting Assistant Professor, Massachusetts Institute of Technology (MIT), MA 2015 { Project researcher (Adjunct Assistant Professor), Kavli IPMU 2013 { Zassenhaus Assistant Professor, The Ohio State University 2012 { 2013 Member, Max Planck Institut f¨urMathematik 2011 { 2012 Postdoctoral Research Fellow, University of British Columbia (Mentors, Jim Bryan and Kai Behrend) 2010 { 2011 Postdoctoral research affiliate Member at Isaac Newton Institute, University of Cam- bridge (Mentor, Richard Thomas) 2006 { 2010 Research and Teaching assistant, University of Illinois at Urbana-Champaign Visiting positions 2016 (Jun { Jul) Member, Institut Henri Pinar´e,Paris, France 2015 (Apr { May) Senior Visiting Fellow, Mathematics Institute at University of Warwick, UK 2013 (May { May) Visiting Scientist, Erwin Schr¨odingerInt. Inst. Math. Phys., Austria 2009 (Jan { May) Visiting Graduate Student, MSRI, Berkeley, CA 2008 (Mar { Mar) Visiting Graduate Student, Institute for Advanced Study (IAS), Princeton, NJ 2007 (Nov { Nov) Visiting Graduate Student, Institute for Advanced Study (IAS), Princeton, NJ Education 2011 Ph.D. Mathematics, University of Illinois at Urbana-Champaign, Urbana, Illinois, USA (Advisors: Sheldon Katz and Tom Nevins) 2008 M.Sc. Mathematics, University of Illinois at Urbana-Champaign, Urbana, Illinois, USA 2004 M.Sc. Mechanical Engineering, Sharif University of Technology, Tehran, IRAN 2003 B.Sc. Mechanical Engineering, Sharif University of Technology, Tehran, IRAN 2003 B.Sc. Civil Engineering, Sharif University of Technology, Tehran, IRAN 1999 Diploma Mathematics and Physics, National Organization of Development of Exceptional Tal- ents (NODET), Tabriz, IRAN, Scientific/Academic honors and awards 2009 , 2010 James D. Hogan and university of Illinois Fellowships 2010 University of Illinois Dissertation Completion Fellowship 2009 David G. Bourgin Fellowship ARTAN SHESHMANI CURRICULUM VITAE 2 2009 Phi Kappa Phi national honor society 2007 , 2009 R.E.G.S 2 Fellowship 2006 , 2008 Department of Mathematics internal Fellowship 2006 { 2009 Outstanding instructor at the University of Illinois (4 consecutive years) 2006 { 2010 NSF graduate student travel awards (5 consecutive years) 2004 Ranked 1'st place in M.Sc. level in M.E. 2003 Brilliant talent award by IRAN's Ministry of Science, Research and Technology. M.Sc. entrance without nationwide exam 2003 Ranked 3'rd place in B.Sc. level (out of 152) in M.E. 2000 Brilliant talent award by IRAN's Ministry of Science, Research and Technology. Per- mission to double major in M.E. and C.E. 1999 Ranked 61'st place in IRAN's nationwide university entrance exam among 500000+ participants Publications Submitted and under review papers 5. Vertical D4-D2-D0 bound states on K3 fibrations and modularity, (with Vincent Bouchard, Thomas Creutzig, Emanuel Diaconescu, Charles Doran, Callum Quigley), 54 pages, (2016), arXiv: 1601.04030. 4. Equivariant Gromov-Witten Invariants of Algebraic GKM Manifolds, (with Melissa Liu), 22 pages, Under review, arXiv:1407.1370. 3. Stable pairs on nodal K3 fibrations, (with Amin Gholampour and Yukinobu Toda), 29 pages, Under review, arXiv:1308.4722. 2. Donaldson-Thomas Invariants of 2-Dimensional sheaves inside threefolds and modular forms, (with Amin Gholampour), 49 pages, Under review, arXiv:1309.0050. 1. Direct calculation of higher rank invariants of stable pairs using the Joyce machinery of stack functions, 49 pages, Under review, arXiv:1107.0295. Published and accepted papers 13. Intersection numbers on the relative Hilbert schemes of points on surfaces, (with Amin Gholampour), 11 pages, Asian J. Math., To Appear (2016), arXiv:1504.01107. 12. Wall-crossing and invariants of higher rank stable pairs, 31 pages, Illinois J. Math., Vol 59, 1, 55-83 (2016), arXiv:1101.2252. 11. Higher rank stable pairs and virtual localization, 40 pages, Comm. Anal. Geom., Vol 24, 1 (2015), arXiv:1011.6342. 2 10. Generalized Donaldson-Thomas Invariants of 2-Dimensional sheaves on local P , (with Amin Gholampour), 29 pages, Adv. Theor. Math. Phys., Volume 19, Number 3, 673-699 (2015), arXiv:1309.0056. ARTAN SHESHMANI CURRICULUM VITAE 3 9. Counting curves on surfaces in Calabi-Yau threefolds, (with Amin Gholampour and Richard P. Thomas), 10 pages, Math. Annalen , Volume 360, Issue 1-2, pp 67-78 (2014), arXiv:1309.0051. 8. Introduction to higher rank theory of stable pairs, 11 pages, AMS Proc. Symp. Pure Math. Vol 85, Amer. Math. Soc. (2012), arXiv:1210.4202. 7. Towards studying the higher rank Pandharipande-Thomas theory of stable pairs, 207 pages. Thesis (Ph.D.)-University of Illinois at Urbana-Champaign (2011). 209 pp. ISBN, 978- 1267-16462-9. 6. Structure and Dynamics of Neutrally Buoyant Rigid Sphere Interacting with Thin Vortex Rings, (with Banavara Shashikanth, Scott David Kelly and Wei Mingjun), 18 pages, J. Math. F. Mech. Vol 12, Issue 3, 335-353, Birkh¨auser-Verlag. (2008). 5. Hamiltonian structure and dynamics of a neutrally buoyant rigid sphere interacting with thin vortex rings, 18 pages, Proc. ECI conf. inter. Trans. Phen. V, F., Therm., Bio., Mat. Space Sci. (2007). 4. Hamiltonian structure for a neutrally buoyant rigid body interacting with N vor- tex rings of arbitrary shape, the case of arbitrary smooth body shape, (with Banavara Shashikanth, Scott David Kelly and Jerrold Marsden), 28 pages. Theor. Comput. F. Dyn. Vol 22 Issue 1, 37-64. (2006). 3. Objectivity of rates of deformation tensors in nonlinear continuum mechanics,(with Reza Naghdabadi), Proc. ASME Conf. (2004). 2. General derivation for conjugate strains of Eshelby-like stress tensors,(with Kambiz Be- hfar and Reza Naghdabadi), Proc. ASME (2004). 1. A thermo elastic solution for functionally graded beams using stress function, (with Mohsen Asghari), Proc. ICCES Conf. (2004). Work in preparation 3. Wallcrossing of stable pairs and torsion sheaf invariants over Quintic threefold, (with Amin Gholampour, Davesh Maulik, Yukinobu Toda and Richard Thomas), 17 pages, In preparation. 2. Global Heterotic/F-theory duals with Wilson line symmetry breaking surfaces, (with Herb Clemens, Stuart Raby and Tony Pantev), 52 pages, In preparation. 1. DT invariants of Linear systems in threefolds and modularity, (with Amin Gholampour), 10 pages, In preparation. Selected invited talks 2016 Apr. Oberwolfach, Germany (MFO), Conference on Moduli Spaces and Modular forms || Feb. Piscataway, New Jersey (Rutgers U.), Geometry, Symmetry and Physics Seminar || Feb. Cambridge, Massachusetts (Harvard), (SMCA), Mathematical Physics Seminar || Jan. Aarhus, Denmark (Center for Quantum Geometry of Moduli Spaces), Seminar (QGM) 2015 Dec. Seoul, Korea (KIAS), Algebraic Geometry lectures I,II,III,IV ARTAN SHESHMANI CURRICULUM VITAE 4 || Dec. Clear Water bay, Hong Kong (HKUST), Algebraic Geometry lectures I,II,III || Nov. Tokyo, Japan (Tokyo U.), Algebraic Geometry Seminar || Oct. Luminy, France (CIRM), Conference on Moduli Spaces in Geometry || Oct. Kyoto, Japan (Kyoto U.), Algebraic Geometry Seminar || Oct. Tokyo, Japan (Kavli IPMU), GTM seminar || July Salt lake city, Utah (U. Utah), AMS Algebraic Geometry Mega Conference || Apr. Oxford, UK (Mathematical Institute), Derived categories and applications symposium || Apr. Warwick, UK (Mathematics Institute), Algebraic Geometry seminar || Mar. Urbana, Illinois (UIUC), Algebraic Geometry Seminar || Feb. Philadelphia, Pennsylvania (UPenn), Math-Physics Joint Seminar || Feb. Columbus, Ohio (OSU), Representations and Lie theory Seminar || Feb. Columbus, Ohio (OSU), Algebraic Geometry Seminar 2013 Oct. New York City, New York (Columbia U.), Gromov-Witten Theory Seminar || Sept Urbana, Illinois (UIUC), Algebraic Geometry Seminar || June Trieste, Italy (SISSA), Conference on Hilbert schemes, sheaves and representations || May Vienna, Austria (Erwin Schr¨odingerInternational Institute for Mathematical Physics), Con- ference on Birational Geometry and Geometric Invariant Theory || May Bonn, Germany (Max Planck Inst.), Seminar on Algebra, Geometry and Physics || Apr. Zurich, Switzerland ( Institut f¨urMathemathik, U. Zurich), Algebraische Geometrie || Feb. Zurich, Switzerland (ETH), Seminar on Algebraic Geometry and Moduli || Feb. Tokyo, Japan (Kavli IPMU), Seminar on Derived category, McKay correspondence and Mirror symmetry 2012 Dec. Piscataway, New Jersey (Rutgers U.), Geometry, Symmetry and Physics Seminar || Dec. College Park, Maryland (U. Maryland), Seminar on Algebra and number theory || Oct. Paris, France (Ecole´ Normale Sup´erieure),Darboux Seminar || Oct. Warwick, UK (Mathematics Institute, U. Warwick), Conference on Homological Projective Duality and Noncommutative Geometry || July Bonn, Germany (Hausdorff center for Mathematics), String-Math 2012 2011 Nov. Cambridge, Massachusetts (Harvard), Harvard/MIT Algebraic Geometry Seminar || Nov. Palo Alto, California (Stanford U.), Algebraic Geometry Seminar || Nov. Berkeley, California (UC Berkeley), Rep. Theory/Geometry/Combinatorics Seminar || June Philadelphia, Pennsylvania (Upenn), String Math 2011 || Apr. Warwick, UK (Mathematical Institute, U.
Recommended publications
  • VITA Sheldon Katz Urbana, IL 61801 Phone
    VITA Sheldon Katz Urbana, IL 61801 Phone: (217) 265-6258 Education S.B. 1976 Massachusetts Institute of Technology (Mathematics) Ph.D. 1980 Princeton University (Mathematics) Professional Experience University of Illinois Professor 2001{ Dean's Special Advisor, College of LAS 2018{ Interim Chair, Department of Mathematics Fall 2017 Chair, Department of Mathematics 2006{2011 Oklahoma State University Regents Professor 1999{2002 Southwestern Bell Professor 1997{1999 Professor 1994{2002 Associate Professor 1989{1994 Assistant Professor 1987{1989 University of Oklahoma Assistant Professor (tenure 1987) 1984{1987 University of Utah Instructor 1980{1984 Visiting Positions MSRI Simons Visiting Professor 2018 Simons Center 2012 Mittag-Leffler Institute, Sweden Visiting Professor 1997 Duke University Visiting Professor 1991{1992 University of Bayreuth, West Germany Visiting Professor 1989 Institute for Advanced Study Member 1982{1983 Publications 1. Degenerations of quintic threefolds and their lines. Duke Math. Jour. 50 (1983), 1127{1135. 2. Lines on complete intersection threefolds with K=0. Math. Z. 191 (1986), 297{302. 3. Tangents to a multiple plane curve. Pac. Jour. Math. 124 (1986), 321{331. 4. On the finiteness of rational curves on quintic threefolds. Comp. Math. 60 (1986), 151{162. 5. Hodge numbers of linked surfaces in P4. Duke Math. Jour. 55 (1987), 89{95. 6. The cubo-cubic transformation of P3 is very special. Math. Z. 195 (1987), 255{257. 7. Iteration of Multiple point formulas and applications to conics. Proceed- ings of the Algebraic Geometry Conference, Sundance, UT 1986, SLN 1311, 147{155. 8. Varieties cut out by quadrics: Scheme theoretic versus homogeneous gen- eration of ideals (with L.
    [Show full text]
  • Mirror Symmetry Is a Phenomenon Arising in String Theory in Which Two Very Different Manifolds Give Rise to Equivalent Physics
    Clay Mathematics Monographs 1 Volume 1 Mirror symmetry is a phenomenon arising in string theory in which two very different manifolds give rise to equivalent physics. Such a correspondence has Mirror Symmetry Mirror significant mathematical consequences, the most familiar of which involves the enumeration of holomorphic curves inside complex manifolds by solving differ- ential equations obtained from a “mirror” geometry. The inclusion of D-brane states in the equivalence has led to further conjectures involving calibrated submanifolds of the mirror pairs and new (conjectural) invariants of complex manifolds: the Gopakumar Vafa invariants. This book aims to give a single, cohesive treatment of mirror symmetry from both the mathematical and physical viewpoint. Parts 1 and 2 develop the neces- sary mathematical and physical background “from scratch,” and are intended for readers trying to learn across disciplines. The treatment is focussed, developing only the material most necessary for the task. In Parts 3 and 4 the physical and mathematical proofs of mirror symmetry are given. From the physics side, this means demonstrating that two different physical theories give isomorphic physics. Each physical theory can be described geometrically, and thus mirror symmetry gives rise to a “pairing” of geometries. The proof involves applying R ↔ 1/R circle duality to the phases of the fields in the gauged linear sigma model. The mathematics proof develops Gromov-Witten theory in the algebraic MIRROR SYMMETRY setting, beginning with the moduli spaces of curves and maps, and uses localiza- tion techniques to show that certain hypergeometric functions encode the Gromov-Witten invariants in genus zero, as is predicted by mirror symmetry.
    [Show full text]
  • Download Enumerative Geometry and String Theory Free Ebook
    ENUMERATIVE GEOMETRY AND STRING THEORY DOWNLOAD FREE BOOK Sheldon Katz | 206 pages | 31 May 2006 | American Mathematical Society | 9780821836873 | English | Providence, United States Enumerative Geometry and String Theory Chapter 2. The most accessible portal into very exciting recent material. Topological field theory, primitive forms and related topics : — Nuclear Physics B. Bibcode : PThPh. Bibcode : hep. As an example, consider the torus described above. Enumerative Geometry and String Theory standard analogy for this is to consider a multidimensional object such as a garden hose. An example is the red circle in the figure. This problem was solved by the nineteenth-century German mathematician Hermann Schubertwho found that there are Enumerative Geometry and String Theory 2, such lines. Once these topics are in place, the connection between physics and enumerative geometry is made with the introduction of topological quantum field theory and quantum cohomology. Enumerative Geometry and String Theory mirror symmetry relationship is a particular example of what physicists call a duality. Print Price 1: The book contains a lot of extra material that was not included Enumerative Geometry and String Theory the original fifteen lectures. Increasing the dimension from two to four real dimensions, the Calabi—Yau becomes a K3 surface. This problem asks for the number and construction of circles that are tangent to three given circles, points or lines. Topological Quantum Field Theory. Online Price 1: Online ISBN There are infinitely many circles like it on a torus; in fact, the entire surface is a union of such circles. For other uses, see Mirror symmetry. As an example, count the conic sections tangent to five given lines in the projective plane.
    [Show full text]
  • String-Math 2012
    Volume 90 String-Math 2012 July 16–21, 2012 Universitat¨ Bonn, Bonn, Germany Ron Donagi Sheldon Katz Albrecht Klemm David R. Morrison Editors Volume 90 String-Math 2012 July 16–21, 2012 Universitat¨ Bonn, Bonn, Germany Ron Donagi Sheldon Katz Albrecht Klemm David R. Morrison Editors Volume 90 String-Math 2012 July 16–21, 2012 Universitat¨ Bonn, Bonn, Germany Ron Donagi Sheldon Katz Albrecht Klemm David R. Morrison Editors 2010 Mathematics Subject Classification. Primary 11G55, 14D21, 14F05, 14J28, 14M30, 32G15, 53D18, 57M27, 81T40. 83E30. Library of Congress Cataloging-in-Publication Data String-Math (Conference) (2012 : Bonn, Germany) String-Math 2012 : July 16-21, 2012, Universit¨at Bonn, Bonn, Germany/Ron Donagi, Sheldon Katz, Albrecht Klemm, David R. Morrison, editors. pages cm. – (Proceedings of symposia in pure mathematics; volume 90) Includes bibliographical references. ISBN 978-0-8218-9495-8 (alk. paper) 1. Geometry, Algebraic–Congresses. 2. Quantum theory– Mathematics–Congresses. I. Donagi, Ron, editor. II. Katz, Sheldon, 1956- editor. III. Klemm, Albrecht, 1960- editor. IV. Morrison, David R., 1955- editor. V. Title. QA564.S77 2012 516.35–dc23 2015017523 DOI: http://dx.doi.org/10.1090/pspum/090 Color graphic policy. Any graphics created in color will be rendered in grayscale for the printed version unless color printing is authorized by the Publisher. In general, color graphics will appear in color in the online version. Copying and reprinting. Individual readers of this publication, and nonprofit libraries acting for them, are permitted to make fair use of the material, such as to copy select pages for use in teaching or research. Permission is granted to quote brief passages from this publication in reviews, provided the customary acknowledgment of the source is given.
    [Show full text]
  • Albion Lawrence CV
    Curriculum Vitae – Albion Lawrence Brandeis University, Dept. of Physics, MS057, POB 549110, Waltham, MA 02454, USA Phone: (781)-736-2865, FAX: (781)-736-2915, email: [email protected] http://www.brandeis.edu/~albion/ Born March 29, 1969 in Berkeley, CA Citizenship U.S.A. Degrees granted The University of Chicago Ph.D. in Physics, 1996. Thesis: “On the target space geometry of N = (2, 1) string theory”. Advisor: Prof. Emil Martinec. University of California, Berkeley A.B. in Physics with highest honors and highest dis- tinction in general scholarship, 1991. Thesis: “Neu- trino optics and coherent flavor oscillations”. Advi- sor: Prof. Mahiko Suzuki. Academic appointments July 2009-present Associate Professor, Brandeis University. 2002-2009 Assistant Professor, Brandeis University. 1999-2002 Postdoctoral Research Associate, Stanford Linear Accelerator Center and Physics Department, Stan- ford University. 1996-1999 Postdoctoral Fellow, Harvard University. 1994-1996 Research Assistant to Prof. Emil Martinec, The Uni- versity of Chicago. 1991-1994 NSF Graduate Fellow, The University of Chicago. 1989-1991 Undergraduate Research Assistant to Prof. Paul Richards, UC Berkeley and Lawrence Berkeley Na- tional Laboratory. Summer 1988 Undergraduate Research Assistant to Prof. William Molzon, University of California, Irvine. Teaching experience August 2002-present Brandeis University. Instructor, graduate and under- graduate quantum mechanics, quantum field theory, cosmology. Winter 1995 Teaching assistant to Prof. Reindardt Oehme, grad- uate quantum mechanics. Awards and Honors Fall 2006 Kavli Frontier Fellow 2004-present DOE Outstanding Junior Investigator award. 1991-1994 NSF Graduate Fellowship. Spring 1990 Inducted into Phi Beta Kappa. 1987-1991 Regent’s Scholar, UC Berkeley. Grants 2007-present Supported by DOE grant DE-FG02-92ER40706.
    [Show full text]
  • References [Bar01] Serguei Barannikov, Quantum Periods, I : Semi-Infinite Variations of Hodge Struc- Tures, Internat
    References [Bar01] Serguei Barannikov, Quantum Periods, I : Semi-Infinite Variations of Hodge Struc- tures, Internat. Math. Res. Not. 23 (2001), 1243{1264. [CdlOGP91] Philip Candelas, Xenia de la Ossa, Paul Green, and Linda Parkes, A pair of Calabi{ Yau manifolds as an exactly soluble superconformal theory, Nucl. Phys. B 359 (1991), no. 1, 21{74. [CFW11] Alberto S. Cattaneo, Giovanni Felder, and Thomas Willwacher, The character map in deformation quantization, Adv. Math. 228 (2011), no. 4, 1966{1989. [CIT09] Tom Coates, Hiroshi Iritani, and Hsian-Hua Tseng, Wall-crossings in toric Gromov- Witten theory I: crepant examples, Geom. Topol. 13 (2009), no. 5, 2675{2744. [CK99] David A. Cox and Sheldon Katz, Mirror Symmetry and Algebraic Geometry, Amer. Math. Soc., 1999. [Cos07] Kevin Costello, Topological conformal field theories and Calabi-Yau categories, Adv. Math. 210 (2007), no. 1, 165{214. [Cos09] , The partition function of a topological field theory, J. Topol. 2 (2009), no. 4, 779{822. [FOOO10] Kenji Fukaya, Yong-Geun Oh, Hiroshi Ohta, and Kaoru Ono, Lagrangian intersec- tion Floer theory - anomaly and obstruction - I, American Mathematical Society, 2010. [FOOO12] Kenji Fukaya, Y G Oh, Hiroshi Ohta, and Kaoru Ono, Lagrangian Floer theory on compact toric manifolds: survey, Surveys in differential geometry. Vol. XVII, Int. Press, Boston, MA, 2012, pp. 229{298. [Get93] Ezra Getzler, Cartan homotopy formulas and the Gauss-Manin connection in cyclic homology, Israel Math. Conf. Proc. 7 (1993), 1{12. [Giv96] Alexander Givental, Equivariant Gromov-Witten invariants, Int. Math. Res. Not. 1996 (1996), no. 13, 613{663. [GPS15] Sheel Ganatra, Tim Perutz, and Nick Sheridan, Mirror symmetry: from categories to curve counts, arXiv:1510.03839 (2015).
    [Show full text]
  • Curriculum Vitae
    Curriculum Vitae Name: Chiu-Chu Melissa Liu Mailing address. Columbia University, Mathematics Department Room 623, Mail Code 4435, New York, NY 10027 Phone: (212) 854-2499 Fax: (212) 854-8962 E-mail Address: [email protected] Major Professional Interests. Algebraic Geometry, Symplectic Geometry Education. Institution Years Major Degree&Date National Taiwan University 1992-1996 Mathematics BS, June 1996 Harvard University 1997-2002 Mathematics PhD, June 2002 PhD thesis advisor: Shing-Tung Yau Pre-doctoral Awards, Honors, and Fellowships. • James K. Whittemore Scholarship at Harvard University, 1997-1998 • Joseph Leonard Walsh Fellowship at Harvard University, 1998-1999 Postdoctoral Awards, Honors, and Fellowships. • Junior Fellowship, Society of Fellows, Harvard University, 2002-2005 • Alfred P. Sloan Research Fellowship, 2007-2009 • Morningside Silver Medal, The 4th International Congress of Chinese Math- ematicians, 2007 Employment. • Junior Fellow, Society of Fellows, Harvard University, 2002 – 2005 • Assistant Professor, Northwestern University, 2005 – 2006 • Associate Professor, Northwestern University, 2006 – 2008 (with tenure) • Associate Professor, Columbia University, 2006 – present (tenured since July 2008) Teaching Experience. I. Undergraduate level: (1) Course Assistant of Applied Mathematics 106. Applied Algebra and Com- binatorics, Fall 1997, Harvard University (2) Teaching Fellow of Mathematics 21b. Linear Algebra and Differential Equa- tions, Spring 1998, Harvard University (3) Course Assistant of Mathematics 274. Mathematical Aspects of String The- ory, Fall 1999, Harvard University (Instructor: Cumrun Vafa) (4) Teaching Fellow of Mathematics 21a. Multivariable Calculus, Fall 2000, Fall 2001, Spring 2002, Harvard University (5) Instructor of Mathematics 290-3. MENU: Linear Algebra and Multivariable Calculus, Spring 2006, Northwestern University (6) Instructor of Math V1201. Calculus III, Fall 2006, Columbia University (7) Instructor of Math V1202.
    [Show full text]
  • Mirror Symmetry and Algebraic Geometry, 1999 67 A
    http://dx.doi.org/10.1090/surv/068 Selected Titles in This Series 68 David A. Cox and Sheldon Katz, Mirror symmetry and algebraic geometry, 1999 67 A. Borel and N. Wallach, Continuous cohomology, discrete subgroups, and representations of reductive groups, Second Edition, 1999 66 Yu. Ilyashenko and Weigu Li, Nonlocal bifurcations, 1999 65 Carl Faith, Rings and things and a fine array of twentieth century associative algebra, 1999 64 Rene A. Carmona and Boris Rozovskii, Editors, Stochastic partial differential equations: Six perspectives, 1999 63 Mark Hovey, Model categories, 1999 62 Vladimir I. Bogachev, Gaussian measures, 1998 61 W. Norrie Everitt and Lawrence Markus, Boundary value problems and symplectic algebra for ordinary differential and quasi-differential operators, 1999 60 Iain Raeburn and Dana P. Williams, Morita equivalence and continuous-trace C*-algebras, 1998 59 Paul Howard and Jean E. Rubin, Consequences of the axiom of choice, 1998 58 Pavel I. Etingof, Igor B. Frenkel, and Alexander A. Kirillov, Jr., Lectures on representation theory and Knizhnik-Zamolodchikov equations, 1998 57 Marc Levine, Mixed motives, 1998 56 Leonid I. Korogodski and Yan S. Soibelman, Algebras of functions on quantum groups: Part I, 1998 55 J. Scott Carter and Masahico Saito, Knotted surfaces and their diagrams, 1998 54 Casper Goffman, Togo Nishiura, and Daniel 'Waterman, Homeomorphisms in analysis, 1997 53 Andreas Kriegl and Peter W. Michor, The convenient setting of global analysis, 1997 52 V. A. Kozlov, V. G. Maz'ya, and J. Rossmann, Elliptic boundary value problems in domains with point singularities, 1997 51 Jan Maly and William P. Ziemer, Fine regularity of solutions of elliptic partial differential equations, 1997 50 Jon Aaronson, An introduction to infinite ergodic theory, 1997 49 R.
    [Show full text]
  • Hilbert Schemes, Donaldson-Thomas Theory, Vafa-Witten and Seiberg Witten Theories by Artan Sheshmani*
    Hilbert Schemes, Donaldson-Thomas Theory, Vafa-Witten and Seiberg Witten Theories by Artan Sheshmani* Abstract. This article provides the summary of 1. Introduction [GSY17a] and [GSY17b] where the authors studied the In recent years, there has been extensive math- enumerative geometry of “nested Hilbert schemes” ematical progress in enumerative geometry of sur- of points and curves on algebraic surfaces and faces deeply related to physical structures, e.g. their connections to threefold theories, and in around Gopakumar-Vafa invariants (GV); Gromov- particular relevant Donaldson-Thomas, Vafa-Witten Witten (GW), Donaldson-Thomas (DT), as well as and Seiberg-Witten theories. Pandharipande-Thomas (PT) invariants of surfaces; and their “motivic lifts”. There is also a tremen- dous energy in the study of mirror symmetry of sur- Contents faces from the mathematics side, especially Homo- logical Mirror Symmetry. On the other hand, phys- 1 Introduction . 25 ical dualities in Gauge and String theory, such as Acknowledgment . 26 Montonen-Olive duality and heterotic/Type II du- 2 Nested Hilbert Schemes on Surfaces . 26 ality have also been a rich source of spectacular 2.1 Special Cases . 27 predictions about enumerative geometry of moduli 2.2 Nested Hilbert Scheme of Points . 27 spaces on surfaces. For instance an extensive re- 3 Nested Hilbert Schemes and DT Theory of search activity carried out during the past years was Local Surfaces . 28 to prove the modularity properties of GW or DT in- References . 30 variants as suggested by the heterotic/Type II dual- ity. The first prediction of this type, the Yau-Zaslow conjecture [YZ96], was proven by Klemm-Maulik- Pandharipande-Scheidegger [KMPS10].
    [Show full text]
  • The Quantum Mckay Correspondence for Polyhedral Singularities
    THE QUANTUM MCKAY CORRESPONDENCE FOR POLYHEDRAL SINGULARITIES JIM BRYAN AND AMIN GHOLAMPOUR ABSTRACT. Let G be a polyhedral group, namely a finite sub- group of SO(3). Nakamura’s G-Hilbert scheme provides a pre- ferred Calabi-Yau resolution Y of the polyhedral singularity C3/G. The classical McKay correspondence describes the classical geom- etry of Y in terms of the representation theory of G. In this paper we describe the quantum geometry of Y in terms of R, an ADE root system associated to G. Namely, we give an explicit formula for the Gromov-Witten partition function of Y as a product over the positive roots of R. In terms of counts of BPS states (Gopakumar- Vafa invariants), our result can be stated as a correspondence: each positive root of R corresponds to one half of a genus zero BPS state. As an application, we use the Crepant Resolution Con- jecture to provide a full prediction for the orbifold Gromov-Witten invariants of [C3/G]. 1. INTRODUCTION Let G be a finite subgroup of SU(3), and let X be the quotient singularity X = C3/G. There is a preferred Calabi-Yau resolution π : Y X → arXiv:0803.3766v2 [math.AG] 31 Jul 2009 given by Nakamura’s G-Hilbert scheme (Definition 6) Y = G -Hilb(C3). The classical McKay correspondence describes the geometry of Y in terms of the representation theory of G [5, 31]. One of the original formulations1 of the correspondence is a bijection of finite sets: Classical McKay Correspondence: ✛ ✲ Irreducible representations of G Geometric basis for H∗(Y, Z).
    [Show full text]
  • Evaluating Tautological Classes Using Only Hurwitz Numbers
    TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY Volume 360, Number 11, November 2008, Pages 6103–6111 S 0002-9947(08)04481-4 Article electronically published on May 22, 2008 EVALUATING TAUTOLOGICAL CLASSES USING ONLY HURWITZ NUMBERS AARON BERTRAM, RENZO CAVALIERI, AND GUEORGUI TODOROV Abstract. Hurwitz numbers count ramified covers of a Riemann surface with prescribed monodromy. As such, they are purely combinatorial objects. Tau- tological classes, on the other hand, are distinguished classes in the intersection ring of the moduli spaces of Riemann surfaces of a given genus, and are thus “geometric”. Localization computations in Gromov-Witten theory provide non-obvious relations between the two. This paper makes one such computa- tion, and shows how it leads to a “master” relation (Theorem 0.1) that reduces the ratios of certain interesting tautological classes to the pure combinatorics of Hurwitz numbers. As a corollary, we obtain a purely combinatorial proof of a theorem of Bryan and Pandharipande, expressing in generating function form classical computations by Faber/Looijenga (Theorem 0.2). Introduction Clever applications of the Atiyah-Bott localization theorem in the context of Gromov-Witten theory have generated volumes of enumerative data as well as many insights into the structure of the tautological rings of the moduli spaces of curves ([FP00], [FP05], [GJV01], [GJV06]). The general idea is to exploit torus actions on a target manifold (often just P1) to obtain torus actions on the moduli spaces of stable maps to the target. An analysis of the fixed loci for the torus action then produces intersection numbers and relations among tautological classes.
    [Show full text]
  • ANDREI CĂLDĂRARU Work Address Home Address Mathematics Department 2817 Van Hise Ave
    ANDREI CĂLDĂRARU Work Address Home Address Mathematics Department 2817 Van Hise Ave. University of Wisconsin-Madison Madison, WI 53705, USA 480 Lincoln Drive Madison, WI 53706-1388, USA Telephone: (608) 262-2880 Telephone: (608) 233-9084 E-mail: [email protected] Web address: http://www.math.wisc.edu/~andreic AREAS OF Algebraic Geometry, String Theory, Homological Algebra INTEREST POSITIONS Vilas Associate Research Professor 2020-2022 HELD Named professor, University of Wisconsin-Madison, WI Professor 2012---present University of Wisconsin-Madison, WI Visiting Invited Professor Fall 2012 Max Planck Institute for Mathematics, Bonn, Germany Tenured Associate Professor 2008---2012 University of Wisconsin-Madison, WI Tenure Track Assistant Professor 2005---2008 University of Wisconsin-Madison, WI NSF Postdoctoral Fellow/University Lecturer 2002---2005 University of Pennsylvania, Philadelphia, PA EDUCATION VisitingPh.D. (Mathematics) Assistant Professor 2000May –2000-2002 UniversityCornell University, of Massachusetts, Ithaca, NY Amherst, MA Areas of interest: algebraic geometry, string theory. Master of Science (Computer Science) May 2000 Cornell University, Ithaca, NY Concentrations: theoretical computer science and cryptography. Bachelor of Science (Mathematics and Computer Science) July 1993 Hebrew University, Jerusalem, Israel Graduated Summa Cum Laude with a double major in mathematics and computer science. PH. D. THESIS Derived categories of twisted sheaves on Calabi-Yau manifolds (Cornell University, 2000) Thesis advisor: Dr. Mark Gross (currently Professor at Cambridge University, England) AWARDS Vilas Associate Research Professorship ($75,000) 2020—2022 Named professorship. NSF Research Grant 1811925 ($250,000) 2018—2022 Research grant for travel, visitors, research expenses, and summer salary. University of Wisconsin Graduate School Grant ($23,466) 2018 Provides summer salary and graduate student support Short term visitor, Institute for Advanced Studies Fall 2016 “Homological Mirror Symmetry” special year program.
    [Show full text]