Institute of Mathematics and Informatics

Семинар по геометрия на МЦМН
2024-12-04 16:00 - 17:30 (Europe/Sofia) | Институт по математика и информатика – БАН, Block 8, 1113 БАН IV км., София, Bulgaria
Следващата сбирка на Семинара по геометрия на МЦМН
ще се проведе в сряда, 4 ДЕКЕМВРИ 2024 г. от 16:00 ч. в зала 403 и онлайн в Zoom:
Доклад на тема
Tropical compactifications of moduli spaces – Part 2

ще изнесе Лайънъл Ланг, Международен център по математически науки (МЦМН – София).

Abstract: In this talk I will describe various tropical compactifications of the moduli spaces of curves. I will discuss some motivations and applications coming from tropical geometry (joint with M. Melo, J. Rau and F. Viviani).

Zoom link:
https://us02web.zoom.us/j/83740034721?pwd=[REDACTED]

Семинар по геометрия на МЦМН
2024-11-27 16:00 - 17:30
Следващата сбирка на Семинара по геометрия на МЦМН
ще се проведе в сряда, 27 ноември 2024 г. от 16:00 ч. в зала 403 и онлайн в Zoom:
Доклад на тема
Tropical compactifications of moduli spaces

ще изнесе Лайънъл Ланг, Международен център по математически науки (МЦМН – София).

Abstract: In this talk I will describe various tropical compactifications of the moduli spaces of curves. I will discuss some motivations and applications coming from tropical geometry (joint with M. Melo, J. Rau and F. Viviani).

Zoom link:
https://us02web.zoom.us/j/83740034721?pwd=[REDACTED]

Семинар по геометрия на МЦМН
2024-05-15 16:00 - 17:30
Следващата сбирка на Семинара по геометрия на МЦМН
ще се проведе в сряда, 15 май 2024 г. от 16:00 ч. в зала 403 и онлайн в Zoom:
Доклад на тема
Hyperbolic amoebas

ще изнесе Михаил Школников, ИМИ – БАН.

Abstract: Classical amoebas serve as a tool to study algebraic varieties and as one of the entry points to tropical geometry. The original definition involves a logarithmic projection of a subvariety of a complex algebraic torus, which can be interpreted as forgetting the phase, i.e. the arguments of complex numbers. In group-theoretic terms, this projection map may be thought of as passing to the quotient by the maximal compact subgroup. Suppose one replaces the algebraic torus with a complex three-dimensional matrix group. In that case, the analogous projection naturally has a three-dimensional hyperbolic space as its target, and it still makes sense to consider images, i.e. hyperbolic amoebas, of complex algebraic varieties under this map. I will review some of the basic properties of hyperbolic amoebas, extending a fascinating interplay between complex and hyperbolic geometries.Based on joint work with Grigory Mikhalkin.

Zoom link:
https://us02web.zoom.us/j/83740034721?pwd=[REDACTED]

Семинар по геометрия на МЦМН
2024-04-24 16:00 - 17:30
Следващата сбирка на Семинара по геометрия на МЦМН
ще се проведе в сряда, 24 април 2024 г. от 16:00 ч. в зала 403:
Доклад на тема
Generalised Plucker formula

ще изнесе Андрей Бенгуш-Ласние, МЦМН.

Abstract: In order to classify objects in singularity theory and algebraic geometry, we define invariants associated to varieties or germs of singularities and hope to have enough tools to compute them easily. From classical projective duality, for any variety (X), we can define a dual variety (X∗) and we call the class of (X) the degree of (X∗). Plücker’s formula allows one to compute this class for plane curves with a certain set of nodes, cusps and tacnodes.
We will start our talk by recalling the general Bézout theorem and then present the Plücker-Teissier formula, which generalises Plücker’s formula to hypersurfaces, and we will sketch a method to generalise the approach to its proof to general complete intersections.

Zoom link:
https://us02web.zoom.us/j/83740034721?pwd=[REDACTED]

Семинар по геометрия на МЦМН
2024-03-27 16:00 - 17:30
Следващата сбирка на Семинара по геометрия на МЦМН
ще се проведе в сряда, 27 март 2024 г. от 16:00 ч. в зала 403:
Доклад на тема
Reading seminar of geometric Lubin-Tate theory

ще изнесе Jiachang Xu, ИМИ – БАН.

Abstract: This is reading seminar of geometry of Lubin-Tate theory, our goal is to understand the papers “M. J. Hopkins and B. H. Gross, Equivariant vector bundles on the Lubin-Tate moduli space” and “Ramero, Lorenzo On a class of étale analytic sheaves”. The first seminar we plan to go over the basis of deformation theory, formal group and necessary rigid geometry.

Zoom link:
https://us02web.zoom.us/j/83740034721?pwd=[REDACTED]

Семинар по геометрия на МЦМН
2024-03-20 16:00 - 17:30
Следващата сбирка на Семинара по геометрия на МЦМН
ще се проведе в сряда, 20 март 2024 г. от 16:00 ч. в зала 403:
Доклад на тема
Ellipsoid superpotentials: obstructing symplectic embeddings by singular algebraic curves

ще изнесе Григори Михалкин, Женевски университет.

Abstract: How singular can be a local branch of a plane algebraic curve of a given degree d? A remarkable series of real algebraic curves was constructed by Stepan Orevkov. It is based on even-indexed numbers in the Fibonacci series: a degree 5 curve with a 13/2 cusp, a degree 13 curve with a 34/5-cusp, and so on. We discuss this and other series of algebraic curves in the context of the problem of symplectic packing of an ellipsoid into a ball, with the answer given by the spectacular Fibonacci staircase of McDuff and Schlenk. The aspect ratio a>1 of the ellipsoid can be viewed as a real parameter for a certain enumerative superpotential function, which is mostly locally constant, but jumps at certain specific rational values (responsible for the aspects of cusp singularities). Based on joint work with Kyler Siegel.

Това заседание на семинара няма да се излъчва в Zoom.

Семинар по геометрия на МЦМН
2024-02-28 16:00 - 17:30
Следващата сбирка на Семинара по геометрия на МЦМН
ще се проведе в сряда, 28 февруари 2024 г. от 16:00 ч. в зала 403 и онлайн в Zoom:
Доклад на тема
Linear embeddings of complex Grassmannians

ще изнесе Иван Пенков, Constructor University Bremen.

Zoom link:

https://us02web.zoom.us/j/83740034721?pwd=[REDACTED]

Abstract: 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.

Семинар по геометрия на МЦМН
2024-02-14 16:00 - 17:30
Следващата сбирка на Семинара по геометрия на МЦМН
ще се проведе в сряда, 14 февруари 2024 г. от 16:00 ч. в зала 403 и онлайн в Zoom:
Доклад на тема
Refined curve counting

ще изнесе Михаил Школников, ИМИ – БАН.

Zoom link:

https://us02web.zoom.us/j/83740034721?pwd=[REDACTED]

Abstract: 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.

Семинар по геометрия на МЦМН
2024-02-07 16:00 - 17:30
Следващата сбирка на Семинара по геометрия на МЦМН
ще се проведе в сряда, 7 февруари 2024 г. от 16:00 ч. в зала 403 и онлайн в Zoom:
Доклад на тема
Introduction to curve counting

ще изнесе Михаил Школников, ИМИ – БАН.

Zoom link:

https://us02web.zoom.us/j/83740034721?pwd=[REDACTED]

Abstract: 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. In the realm of classical planimetry, we know that there exists a single circle passing through a collection of three points, provided that these points are generic. Here “generic” simply means that the points are not collinear, i.e. don’t belong to the same line but could refer to some other open condition in a different context; the number of points is just right for a problem to be well-stated — there are infinitely many circles passing through any two points and a collection of four points lying on a circle is special. A less trivial example, which will be considered in detail, is the question “How many rational cubic curves on the plane pass through a generic collection of eight points?”. “Rational” here means that a curve has a parametrization by rational functions, and “cubic” refers to a curve defined as a zero locus of a degree three polynomial. The number of points is again chosen just right so that one may expect a non-trivial answer. In the case of real algebraic geometry, the number of cubics may vary depending on the position of the eight generic points, and a priori it is even not clear if such curves exist for all configurations. On the other hand, if we state the same problem over complex numbers the answer becomes definite and independent of the position of the generic points. By an elegant, yet quite elementary, topological reasoning we will deduce that this answer is 12. Adapting the same argument in the real case, we will see that real rational cubics should be counted with signs and the result of this new count becomes a definite -8, proving in particular that for any generic configuration of eight points on the real plane, there exist at least eight rational real cubics passing through them.

Семинар по геометрия на МЦМН
2024-01-31 16:00 - 17:30
Следващата сбирка на Семинара по геометрия на МЦМН
ще се проведе в сряда, 31 януари 2024 г. от 16:00 ч. в зала 403 и онлайн в Zoom:
Доклад на тема
Derived Deformation Theory and Formal Moduli Problem

ще изнесе Инди Чин, МЦМН и ИМИ – БАН.

Zoom link:

https://us02web.zoom.us/j/83740034721?pwd=[REDACTED]

Abstract: 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.

Семинар по геометрия на МЦМН
2024-01-24 16:00 - 17:30
Следващата сбирка на Семинара по геометрия на МЦМН
ще се проведе в сряда, 24 януари 2024 г. от 16:00 ч. в зала 403 и онлайн в Zoom:
Доклад на тема
Introduction to Derived Algebraic Geometry and deformation theory

ще изнесе Инди Чин, ИМИ – БАН.

Zoom link:

https://us02web.zoom.us/j/83740034721?pwd=[REDACTED]

Семинар по геометрия на МЦМН
2023-12-13 16:00 - 17:30
Следващата сбирка на Семинара по геометрия на МЦМН
ще се проведе в сряда, 13 декември 2023 г. от 16:00 ч. в зала 403 и онлайн в Zoom:
Доклад на тема

Valuations of Higher Rank
ще изнесе Андрей Бенгуш-Ласние, Международен център по математически науки (МЦМН – София).

Zoom link:

https://us02web.zoom.us/j/83740034721?pwd=[REDACTED]

Семинар по геометрия на МЦМН
2023-12-06 16:00 - 17:30
Следващата сбирка на Семинара по геометрия на МЦМН
ще се проведе в сряда, 6 декември 2023 г. от 16:00 ч. в зала 403 и онлайн в Zoom:
Доклад на тема

Introduction to tropical modifications (II)
ще изнесе Никита Калинин, Международен център по математически науки (МЦМН – София).

Zoom link:

https://us02web.zoom.us/j/83740034721?pwd=[REDACTED]

Семинар по геометрия на МЦМН
2023-11-22 16:00 - 17:30
Следващата сбирка на Семинара по геометрия на МЦМН
ще се проведе в сряда, 22 ноември 2023 г. от 16:00 ч. в зала 403 и онлайн в Zoom:

Topics in non-archimedean analytic geometry (II)

by Jiachang Xu – International Center for Mathematical Sciences (ICMS – Sofia)

Zoom link:

https://us02web.zoom.us/j/83740034721?pwd=[REDACTED]

Семинар по геометрия на МЦМН
2023-11-15 16:00 - 17:30
Следващата сбирка на Семинара по геометрия на МЦМН
ще се проведе в сряда, 15 ноември 2023 г. от 16:00 ч. в зала 403 и онлайн в Zoom:

Topics in non-archimedean analytic geometry (I),
by Jiachang Xu – International Center for Mathematical Sciences (ICMS – Sofia)

Zoom link:

https://us02web.zoom.us/j/83740034721?pwd=[REDACTED]
