Vesselin Petkov is a professor emeritus ат the University of Bordeaux who has made important contributions to hyperbolic partial differential equations, spectral and scattering theory and dynamical systems.
A seminar talk by Morgan Brown, University of Miami.
A linear embedding of Grassmannians, one of which could possibly be isotropic, is an embedding which respects the generators of Picard groups. Several years ago A.S. Tikhomirov and I classified such embeddings when both Grassmannians are simultaneously usual Grassmannians or isotropic Grassmannians of the same type(orthogonal or symplectic). In this talk I will discuss also the mixed case. A classification as above has an application to the classification of infinite-dimensional linear ind-Grassmannians, and I shall briefly explain this at the end of the talk.
Refining an enumerative problem upgrades the numerical solution to a polynomial so that its specialization gives the original number. A prototypical example of such refinement arises in the tropical curve counting from replacing Mikhalkin multiplicities, corresponding to counting complex curves, with Block-Goettsche multiplicities. I will speak about the invariance of this count and its various interpretations.
I will present a form of quantum circuit complexity that extends to open systems. To illustrate the methodology, I focus on a basic model where the Hilbert space of states is represented by the Euclidean plane. Specifically, the investigation is about the dynamics of mixed quantum states as they undergo interactions with a sequence of gates.
The mirror symmetry phenomenon was discovered by string theorists more than thirty years ago as an equivalence of two physical theories associated with very different geometries. The categorical point of view on this remarkable conjecture was famously introduced by M. Kontsevich in his 1994 ICM talk. As it became clear over time, homological mirror symmetry provides new approaches to many topics in symplectic and algebraic geometry. In these two talks, I will present a brief overview of the conjecture as well as some results inspired by mirror symmetry and obtained in joint work with L. Katzarkov about classical problems on discriminants and singularity theory.
This talk is intended as a very gentle introduction to the classical subject of enumerative geometry concerned with problems of counting algebraic curves with prescribed properties.
Derived deformation theory studies the formal neighborhoods of moduli spaces. The classical work of Kodaira-Spencer on deformation of complex manifolds tells that the dg Lie algebra A^(0,*)(X,TX) controls the deformations of the complex manifold. The example illustrates the following general principle: A dg Lie algebra gives rise to a deformation functor by considering the Maurer-Cartan elements of the dg Lie algebra tensoring with the maximal ideal of an Artin local ring. This idea is explored by many people, including Quillen, Deligne, Drinfeld, Kapranov and Kontesevich. Later, Lurie and Pridham independently proved that the category of dg Lie algebra is indeed equivalent to the category of Formal Moduli problem. I will state their results and explain the idea of the proof.
This is the second talk about tropical modifications. During the first I explained the motivation for using tropical modifications while studying tropical curves and maps between them. In the second talk I will define modifications of the tropical plane and explain how tropical planar curves are changed. Also I show how this can be used in studying inflection points (following the work of E. Brugalle and L. Lopez de Medrano).
A talk by Carlos Varea, (Universidade Tecnológica Federal do Paraná - Campus Cornélio Procópio, Brazil) on January 16, 14:00 Sofia time.
International Center for Mathematical Sciences
Institute of Mathematics and Informatics
Bulgarian Academy of Sciences
Acad. G. Bonchev St. bl.8
1113 Sofia, Bulgaria
Tel. +359 2 9793822
icms-office@math.bas.bg
Copyright 2020 ICMS | All Rights Reserved
