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So far tbranzov has created 112 blog entries.
12 02, 2024

Refined curve counting, a talk by Mikhail Shkolnikov

2024-02-12T09:51:35+02:00February 12th, 2024|Geometry Seminar|

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.

8 02, 2024

Quantum circuit complexity for light polarisation or complexity with no complex number, talk by Jean-Pierre Gazeau

2024-02-12T09:43:47+02:00February 8th, 2024|ICMS Seminar, News|

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.

2 02, 2024

A categorical view of singularity theory I and II, talks by Paul Horja

2024-02-02T12:36:00+02:00February 2nd, 2024|ICMS Seminar, News|

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.

29 01, 2024

Derived Deformation Theory and Formal Moduli Problem, by Yingdi Qin

2024-01-29T09:27:54+02:00January 29th, 2024|Geometry Seminar|

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.

19 01, 2024

Introduction to Derived Algebraic Geometry and deformation theory, by Yingdi Qin

2024-01-19T10:14:47+02:00January 19th, 2024|Geometry Seminar|

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).

12 01, 2024

The H-flux on flag manifolds generated by infinitesimal T-duality, talk by Carlos Varea

2024-01-12T13:04:33+02:00January 12th, 2024|ICMS Seminar, News|

A talk by Carlos Varea, (Universidade Tecnológica Federal do Paraná - Campus Cornélio Procópio, Brazil) on January 16, 14:00 Sofia time.

10 01, 2024

Nilpotent algebras, groups and beyond, talk by Yuri Bahturin

2024-01-15T14:38:13+02:00January 10th, 2024|ICMS Seminar, News|

We study various correspondences between finite-dimensional nilpotent algebras and (quasi)groups similar to those given by the circle product in the case of associative algebras or by the Baker-Campbell-Hausdorff formulas in the case of Lie algebras or their generalizations. In the particular case of Malcev's correspondence, we obtain some new results about groups using Lie algebras and vice versa.

4 01, 2024

The Milnor number of a smoothable curve, talk by Antony Rangachev

2024-01-04T12:32:11+02:00January 4th, 2024|ICMS Seminar, News|

In this talk I will derive an algebraic formula for the Milnor number of a smoothable complex analytic curve singularity X by relating it to the Euler characteristic of its smoothing, which in turn I will relate to the multiplicity of the Jacobian ideal of X and and the multiplicity of X at its singular point. If time permits I will discuss generalizations to higher dimensions. This is a report on a joint work with Gaffney and Bengus-Lasnier.

4 01, 2024

Stratified Morse theory and the critical locus of a linear functional, talk by Antony Rangachev

2024-01-04T12:29:00+02:00January 4th, 2024|ICMS Seminar, News|

In this talk I will use stratified Morse theory to relate the number of critical points of a generic linear functional on a complex analytic manifold M to the Euler characteristics of M and a generic hyperplane slice of M.

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