University of Haifa Distinguished Lectures in Mathematics: Maxim Kontsevich

YouTube Links: Lecture One , Lecture Two , Lecture Three. 

The event was hosted by the  Mathematics Department of the University of Haifa.

Notes of talks below:

The lecture series this year will take place on Zoom the 16th, 17th and 18th of March 2021.  All lectures will be at the same time on each of the three days.

Starting time for all three days

 ISRAEL:  17:00 

               FRANCE:  16:00

US EAST COAST: 11:00

US WEST COAST: 8:00

                HAWAII: 5:00 (sorry)

LONDON (GMT): 15:00

SEOUL: 23:59

TOKYO: 23:59

Title: Quantum Spectrum in Algebraic Geometry

Abstract:  The name 'Quantum Spectrum' in the title refers (for a compact symplectic manifold) to the spectrum of the operator of quantum multiplication by the first Chern class of the tangent bundle plus a correction in degrees 4 and higher, considered as a multi-valued function on the Frobenius manifold encoding genus=0 Gromov-Witten invariants.

In the algebraic case, for complex projective varieties, one of the greatest not yet understood mysteries known from early days of mirror symmetry, is a conjectural relation (by S.Barannikov, B.Dubrovin and myself) between the quantum spectrum and certain semi-orthogonal decomposition of the derived category of coherent sheaves. We are very far from even approaching this problem in complete generality, beyond particular explicit examples.

The main goal of the lectures is the formulation of quantum blow-up formula which seems to be totally within reach, leading to numerous consequences in the mainstream algebraic geometry

One application is the construction of a new very strong birational invariant (also for non-algebraically closed base fields). In particular, one can deduce non-rationality of a generic cubic 4-fold over complex numbers. Another application is a construction of a new exotic motivic measure. More speculatively, one can have a relation to Minimal Program, a categorification of intersection cohomology, and an obstruction to the strong resolution of singularities in positive characteristic. 

Finally, the combination of the  quantum blow-up formula with the semi-continuity of Steenbrink spectra lead to new non-rationality criteria in any dimension.

Previous speakers of the distinguished lecture series:

·       Pierre Cartier (IHES)                               - 2000

·       David Kazhdan (Harvard)                    - 2001

·       Shlomo Sternberg (Harvard)               - 2002

·       Joseph Bernstein (Tel-Aviv)                 - 2003

·       Hillel Furstenberg (Hebrew U.)           - 2004

·       Peter Sarnak (Princeton/NYU)            - 2005

·       Yitzhak Katzenelson (Stanford)           - 2006

·       Matthias Kreck (Bonn)                             - 2008

·       Bela Bolobas (Cambridge)                      - 2009

·       Efim Zelmanov (UC San Diego)           - 2010

·       Vladimir Voevodsky (IAS)                       - 2011

·       Alan Weinstein (Berkeley)                      - 2012

·       Peter Teichner (MPI & Berkeley)          - 2013

·       Endre Szemeredi (Hungarian Ac. Sci)  -2014

·       Yaakov Sinai (Princeton)                           – 2015

·       Claire Voisin (College de France)         – 2016

·       John Morgan (SUNY Stonybrook)     – 2017

·       Barry Simon (Caltech)                               – 2018

·       Phillip Griffiths (IAS)                                  -2019

Return to the home page of Oren Ben-Bassat. Questions about the lecture series? Please write me at oren.benbassat@gmail.com.  If you are interested in applying for a postdoc or graduate student position with me please write me at ben-bassat@math.haifa.ac.il .