Dragos Oprea. Web:

Transcription

1 Dragos Oprea Contact Information: University of California San Diego Work Phone: (858) Gilman Drive # doprea@math.ucsd.edu La Jolla, CA, 92093, USA Web: Research Algebraic geometry, mathematical physics. My research focuses on moduli theory, in particular, the moduli spaces of stable morphisms and stable sheaves, Gromov-Witten and Donaldson-type invariants Employment University of California, San Diego Professor, present Associate Professor, Assistant Professor, Stanford University Szegö Assistant Professor, Samuelson Fellow, Education Massachusetts Institute of Technology Ph.D. in Mathematics, June Thesis advisor: Gang Tian Thesis title: The tautological classes of the moduli spaces of stable maps to flag varieties Harvard University A. B., June 2000, Summa Cum Laude in Mathematics Visits Mathematical Sciences Research Institute, Berkeley, January - April 2009 Isaac Newton Institute, Cambridge, April, June 2011 Centre de Recerca Matematica, Barcelona, June 2012 Max Planck Institute, Bonn, July 2012 Institut Henri Poincaré, Paris, July 2014 ETH, Zürich, April - May 2015 Awards and Fellowships NSF CAREER Grant, Alfred P. Sloan Research Fellowship, NSF Grant for the project The geometry of the moduli spaces of morphisms and sheaves, DMS , Hellman Fellowship,

2 NSA Grant for the project Stable Maps, Stable Sheaves, Stable Quotients, , (awarded but declined) NSF Grant for the project Moduli Spaces of Morphisms and Sheaves, DMS , Housman Award for Excellence in Teaching, May 2005 Cue Certificate for Distinction in Teaching, Harvard University, 1997 Putnam Mathematical Competition, Putnam Fellow 1996; ranked top 25 and member of the Putnam Winning Team, 1997, 1998 International Mathematical Olympiad - 4 medals, Balkan Mathematical Olympiad - 2 medals, Romanian Mathematical Olympiad - 4 medals Publications 1. Divisors on the moduli spaces of stable maps to flag varieties and reconstruction, Journal für die Reine und Angewandte Mathematik 586 (2005), The tautological rings of the moduli spaces of stable maps, Journal of Algebraic Geometry 15 (2006), Tautological classes on the moduli spaces of stable maps to projective spaces via torus actions, Advances in Mathematics 207 (2006), On the intersection theory of the moduli spaces of rank two vector bundles, with Alina Marian, Topology 45 (2006), Virtual intersections on the Quot scheme and Vafa-Intriligator formulas, with Alina Marian, Duke Mathematical Journal 136 (2007), Counts of maps to the Grassmannian and intersections on the moduli space of stable bundles, with Alina Marian, Journal of Differential Geometry 76 (2007), The level-rank duality for non-abelian theta functions, with Alina Marian, Inventiones Mathematicae 168 (2007), A tour of theta dualities on moduli spaces of sheaves, with Alina Marian, Curves and abelian varieties, , Contemporary Mathematics, American Mathematical Society, Providence, Rhode Island 465 (2008) 9. Sheaves on abelian surfaces and Strange Duality, with Alina Marian, Mathematische Annalen 343 (2009), A note on the Verlinde bundles on elliptic curves, Transactions of the American Mathematical Society 362 (2010), GL Verlinde numbers and the Grassmann TQFT, with Alina Marian, Proceedings of the 2009 Lisbon Geometry Summer School, Portugaliae Mathematica 67 (2010), The Verlinde bundles and the semihomogeneous Wirtinger duality, Journal für die Reine und Angewandte Mathematik 567 (2011), The moduli space of stable quotients, with Alina Marian and Rahul Pandharipande, Geometry and Topology 15 (2011), Generic strange duality for K3 surfaces, with Alina Marian, appendix by Kota Yoshioka, Duke Mathematical Journal 162 (2013), Framed sheaves over threefolds and symmetric obstruction theories, Documenta Math 18 (2013),

3 16. On the strange duality conjecture for abelian surfaces, with Alina Marian, Journal of the European Mathematical Society 16 (2014), On Verlinde sheaves and strange duality over elliptic Noether-Lefschetz divisors, with Alina Marian, Annales Institut Fourier 64 (2014), The first Chern class of the Verlinde bundles, with Alina Marian and Rahul Pandharipande, String-Math Proceedings, Bonn 2012, , American Mathematical Society, Providence, Rhode Island 90 (2015) 19. Notes on the moduli space of stable quotients, Compactifying Moduli Spaces, Advanced Courses in Mathematics, , Birkhauser, The Chern character of the Verlinde bundle over M g,n, with Alina Marian, Rahul Pandharipande, Aaron Pixton and Dimitri Zvonkine, Journal für die Reine und Angewandte Mathematik, accepted 21. On the strange duality conjecture for abelian surfaces II, with Barbara Bolognese, Alina Marian, and Kota Yoshioka, Journal of Algebraic Geometry, accepted 22. Segre classes and Hilbert schemes of points, with Alina Marian and Rahul Pandharipande, Annales Scientifiques de l ENS, accepted 23. Bundles of generalized theta functions on abelian surfaces, submitted, available at Teaching University of California, San Diego: Math 10C: Multivariable Calculus (Fall 2009, Winter 2010) Math 20C: Multivariable Calculus for Science and Engineering (Fall 2011) Math 20D: Differential Equations (Fall 2008, Fall 2011) Math 31H: Honors Linear Algebra and Multivariable Calculus (Fall 2010, Winter 2011, Spring 2013, Fall 2013, Winter 2014, Spring 2014) Math 102: Applied Linear Algebra (Winter 2013) Math 104A: Number Theory (Fall 2014) Math 140AB: Foundations of Real Analysis (Spring 2013, Fall 2014, Winter 2015) Math 200A: Graduate Algebra (Fall 2010) Math 203: Algebraic Geometry (Fall 2008, Fall 2009, Winter 2010, Fall 2012, Fall 2015) Math 207: Derived Categories (Spring 2012) Math 220: Complex Analysis (Fall 2015) Math 259: Enumerative Geometry and Moduli Theory (Winter 2011) Math 259: Riemann Surfaces and Algebraic Curves (Winter 2014) Math 259: K3 surfaces (Winter 2015) Math 199/299: Supervised Reading and Research (Spring Fall 2015) Stanford University: Math 51: Linear Algebra and Multivariable Calculus (Fall 2005, Winter 2007) Math 52: Multivariable Integration (Fall 2007) Math 106: Complex Analysis (Fall 2006)

4 Math 145: Undergraduate Algebraic Geometry (Spring 2008) Math 244: Riemann Surfaces and Algebraic Curves (Spring 2008) Math 245: Topics in Moduli Theory (Fall 2006) Math 360: Supervised Reading and Research (Fall 2007) M.I.T., Office of Minority Education: Project Interphase: Calculus (Summer 2003, Summer 2004, Summer 2005) Students Service Perry Strahl (graduate, current) Daniel Schultheis (graduate, Ph.D. 2012). Thesis: Virtual invariants of Quot schemes over del Pezzo surfaces, Arizona and Minnesota (postdoc), Smith College (current) Shishir Agrawal (undergraduate, Highest Honors, 2011). Thesis: Euler characteristics of moduli spaces of stable maps Gregory Edwards (undergraduate, High Honors, 2013). Thesis: On genus zero stable maps to flag varieties M.I.T., Summer Program in Undergraduate Research and Research Summer Institute. Research projects supervised: Jason Chiu, On the area of two-dimensional lattice polytopes Pavlo Pylyavskyy, The Euler characteristics of some Betti moduli spaces Peter Kevei, Arithmetic properties of Bell and Stirling numbers Editorial Board of International Mathematics Research Notices Refereed more than 30 papers for Sigma, Handbook of Moduli, Proceedings of the AMS, European Journal of Mathematics, Communications in Analysis and Geometry, Journal of the London Mathematical Society, International Mathematics Research Notices, Pacific Journal of Mathematics, Compositio Mathematica, Michigan Mathematical Journal, Journal für die Reine und Angewandte Mathematik, Mathematische Annalen, Algebraic Geometry, Journal of Algebraic Geometry, Advances in Mathematics, Geometry and Topology, Duke Math Journal, Inventiones Mathematicae, Annals of Mathematics, Journal of the American Mathematical Society Reviewer, Math Reviews and Zentralblatt Math Reviewer and Panelist: NSA (4 times), NSF (4 times), Portugal Foundation for Science (1 time) Seminars (co)-organized: UCSD Algebraic Geometry Seminar Southern California Algebraic Geometry Seminar Stanford Algebraic Geometry Seminar Berkeley-Stanford Algebraic Geometry Colloquium. Conferences (co)-organized: AMS Sectional Meeting Geometry of Moduli Spaces of Sheaves, Spring 2012 Western Algebraic Geometry Symposium, Fall 2013 Current Developments in Moduli Theory, Fall 2014 Complex Algebraic Geometry, Winter 2015

5 High School Outreach: San Diego Honors Math Competition (5 times) San Diego Math League San Diego Math Circle S.T. Yau Math Competition Hiring Committee, UC San Diego (2 times) Graduate Admissions, UC San Diego (4 times) Graduate committees: Doctoral Committee (UCSD): Dan Budreau, Shaunak Das, Karl Fredricson, Amy Irwin, Daniel Schultheis, Peter Overholser, Brandon Meredith, Mandy Cheung, Michael Kasa, Calum Spicer, Rob Won, Perry Strahl, Jonathan Conder, Yi Li (Physics) Doctoral Committee (Stanford): Jarod Alper, Robert Easton, Huai-Lian Chang, Baosen Wu, Asimina Arvanitaki (Physics) Qualifying Committe (Stanford): Nicola Penev, Huai-Lian Chang, Jack Hall, Baosen Wu, Yu-jong Tzeng, Ziyu Zhang Algebra Qualifying Committee, UC San Diego Student Diversity Committee, UC San Diego Undergraduate and Graduate School Advising, UC San Diego Undergraduate Advising, Stanford University Invited Talks Lausanne, Workshop on Curves on surfaces and 3-folds UCSD, Algebra, Algebraic Geometry and Number Theory RTG Colloquium Columbia University, Algebraic Geometry Seminar University of Utah, AMS Sectional Meeting ETH Zürich, Algebraic Geometry and Moduli Seminar Stony Brook, Algebraic Geometry Seminar University of Kansas, Colloquium UC Los Angeles, Algebraic Geometry Seminar CRIM, Luminy, Workshop on Moduli Spaces ETH Zürich, Algebraic Geometry Lecture Series Humboldt University, Algebraic Geometry Seminar Harvard University, Harvard-MIT Algebraic Geometry Seminar University of Utah, Algebraic Geometry Seminar University of California, Davis, Geometry and Topology Seminar University of British Columbia, Geometry and Physics Seminar University of California, Riverside, AMS Sectional Meeting Yangyang, South Korea, Summer School on Algebraic Geometry Centre de Recerca Matematica Barcelona, School on Compact Moduli Spaces

6 Busan, South Korea, Workshop on Moduli and Birational Geometry Max Planck Institute Bonn, Algebraic Geometry Seminar Centre de Recerca Matematica Barcelona, Geometry Seminar University of Washington, Western Algebraic Geometry Symposium University of Hawaii, AMS Sectional Meeting The Ohio State University, Algebraic Geometry Seminar University of Tokyo, Conference on Arithmetic and Algebraic Geometry Texas Tech, Texas Geometry and Topology Conference University of British Columbia, Algebraic Geometry Seminar Columbia University, Conference on Moduli Theory and Moduli Stacks University of Cambridge, Algebraic Geometry Seminar Isaac Newton Instiute, Algebraic Geometry Seminar Romanian Mathematical Society, Congress of Romanian Mathematicians Korean Institute of Advanced Studies, Workshop on Moduli and Periods Caltech, Algebraic Geometry Seminar Northeastern University, Algebraic Geometry Seminar Australian National University, Algebraic Geometry Conference Caltech, Algebraic Geometry Seminar Princeton University, Algebraic Geometry Seminar University of Illinois at Chicago, Algebraic Geometry Seminar Columbia University, Algebraic Geometry Seminar Stony Brook, Algebraic Geometry Seminar The Ohio State University, Michigan/UIC/OSU Workshop IMPA Rio de Janeiro, Minicourse Stanford University, Algebraic Geometry Seminar UC Riverside, AMS Sectional Meeting Washington University, Saint Louis, Colloquium UCLA, Geometry Seminar University of Arizona, Algebraic Geometry Seminar University of Arizona, Colloquium Beijing University, Symplectic Geometry and Physics Conference MSRI, Modern Moduli Theory Conference Madrid, Conference on vector bundles in honor of S. Ramanan UC Santa Cruz, Algebraic Geometry Seminar UC Davis, Algebraic Geometry Seminar Caltech, Algebraic Geometry Seminar Johns Hopkins University, Algebraic Geometry Seminar

7 Princeton University, Algebraic Geometry Seminar Duke University, Colloquium Rutgers University, Colloquium University of Pittsburgh, Colloquium University of Wisconsin Madison, Colloquium UC San Diego, Colloquium University of Illinois Urbana-Champaign, Colloquium UC Santa Cruz, Colloquium University of Southern California, Colloquium Rice University, Colloquium UC Irvine, Colloquium University of Washington, Western Algebraic Geometry Seminar University of Arizona, AMS Sectional Meeting UC Davis, Colloquium University of Illinois at Chicago, Algebraic Geometry Seminar University of Chicago, Algebraic Geometry Seminar Cologne University, Workshop on Moduli Spaces and Arcs Stanford University, Symplectic Geometry Seminar Stanford University, Algebraic Geometry Seminar UC Berkeley, Algebraic Geometry Seminar Rice University, Algebraic Geometry Seminar Stanford University, Algebraic Geometry Seminar University of Washinghton, Summer Research Institute in Algebraic Geometry Boston University, Algebraic Geometry Seminar Yale University, Algebraic Geometry Seminar University of Pennsylvania, Algebraic Geometry Seminar Johns Hopkins University, Geometry Seminar Harvard University, Geometry Seminar.