**University of Miami**

** Department of Mathematics**

**Lecture Series**

**Professor Maxim Kontsevich**

*Institut des Hautes Études Scientifiques*

University of Miami

Recipient of a Fields Medal in 1998

Winner of the Crafoord Prize in 2008

University of Miami

Recipient of a Fields Medal in 1998

Winner of the Crafoord Prize in 2008

**will present**

**Motivic Donaldson-Thomas Theory**

**Introductory Lecture**

Wednesday, January 16, 2008, 2:15pm to 3:35pm in Ungar Room 402

**Continuing Lectures**

Wednesday, January 30, 2008, 2:15pm to 3:35pm in Ungar Room 402

Wednesday, February 6, 2008, 2:15pm to 3:35pm in Ungar Room 402

Wednesday, February 13, 2008, 2:15pm to 3:35pm in Ungar Room 402

Thursday, February 21, 2008, 5:00pm to 6:00pm in Ungar Room 506

Refreshments served 30 minutes before each talk in Ungar Room 521*All interested persons are welcome to attend.*

**Description:** One of the most interesting functions arising in string theory is the generating series for so-called BPS states on 3-dimensional Calabi-Yau manifold. In mathematical terms this corresponds to Donaldson-Thomas invariants, counting holomorphic vector bundles or (by mirror symmetry) special Lagrangian submanifolds. Gromov-Witten invariants (numbers of holomorphic curves) form just a small part of this new data. The goal of my course is to give an introduction to a very general purely algebraic theory developed recently by Y. Soibelman and myself. It has many aspects, from elementary geometry related to convexity, to triangulated categories, motives, Milnor fibers in singularity theory, non-archimedean geometry, isomonodromy deformations, quantum dilogratihm and cluster algebras.

*Some information about the lecturer:*

*Some information about the lecturer:*

Maxim Kontsevich (IHES, U of M) is one of the leading geometers of our time. His main mathematical contributions: HMS, the proof of Witten's conjecture, the proof of Deligne's conjecture and deformation and quantization have revolutionized the use of abstract category theory and homological algebra in theoretical physics.

He received a Fields Medal in 1998 at the 23rd International Congress of Mathematicians in Berlin, and this year he won the Crafoord Prize. He has had numerous offers from many institutions (IAS included) and is a member of French Academy of Sciences and of Legion d'Honneur.