The next session of the Geometry Seminar of ICMS will be held on Wednesday, April 30, 2025, at 4:00 pm, in room 403 and via Zoom. A talk on: Binary Quadratic Forms and Conway’s Topographs (Lecture 1 of 3) will be delivered by Nikita Kalinin, Guangdong Technion Israel Institute of Technology. The next two lectures will be held on 07.05.2025 and 14.05.2025 at 4:00 pm. Abstract: Binary quadratic forms are as elementary as they are mysterious—much like prime numbers. In 1997, John Conway introduced topographs, a powerful geometric tool that provides a geometric visualization of binary quadratic forms and their values. These lectures will explore how topographs, combined with telescoping summation techniques, yield elegant formulas — some with intuitive geometric interpretations. For instance, consider [...]

The next session of the Geometry Seminar of ICMS will be held on Wednesday, December 4, 2024, at 4:00 pm, in room 403 and via Zoom. A talk on: Tropical compactifications of moduli spaces - Part 2 will be delivered by Lionel Lanf, International Center of Mathematical Sciences (ICMS - Sofia). 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=VnBtcVpGUktscHQ4a09jZkNZTURyZz09  

The next session of the Geometry Seminar of ICMS will be held on Wednesday, November 27, 2024, at 4:00 pm, in room 403 and via Zoom. A talk on: Tropical compactifications of moduli spaces will be delivered by Lionel Lanf, International Center of Mathematical Sciences (ICMS - Sofia). 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=VnBtcVpGUktscHQ4a09jZkNZTURyZz09  

The next session of the Geometry Seminar of ICMS will be held on Wednesday, May 15, 2024, at 16:00, in room 403 and via Zoom. A talk on: Hyperbolic amoebas will be delivered by Mikhail Shkolnikov, IMI - BAS. 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 [...]

The next session of the Geometry Seminar of ICMS will be held on Wednesday, March 20, 2024, at 16:00, in room 403 and via Zoom. A talk on: Generalised Plucker formula will be delivered by Andrei Benguş-Lasnier, ICMS - Sofia. 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 [...]

The next session of the Geometry Seminar of ICMS will be held on Wednesday, March 20, 2024, at 16:00, in room 403 and via Zoom. A talk on: Reading seminar of geometric Lubin-Tate theory will be delivered by Jiachang Xu, IMI - BAS. 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=VnBtcVpGUktscHQ4a09jZkNZTURyZz09  

The next session of the Geometry Seminar of ICMS will be held on Wednesday, March 20, 2024, at 16:00, in room 403 and via Zoom. A talk on: Ellipsoid superpotentials: obstructing symplectic embeddings by singular algebraic curves will be delivered by Grigory Mikhalkin, University of Geneva. 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 [...]

The next session of the Geometry Seminar of ICMS will be held on Wednesday, February 28, 2024, at 16:00, in room 403 and via Zoom. A talk on: Linear embeddings of complex Grassmannians will be delivered by Ivan Penkov, Constructor University Bremen. Zoom link: https://us02web.zoom.us/j/83740034721?pwd=VnBtcVpGUktscHQ4a09jZkNZTURyZz09 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 [...]

The next session of the Geometry Seminar of ICMS will be held on Wednesday, February 7, 2024, at 16:00, in room 403 and via Zoom. A talk on: Refined curve counting will be delivered by Mikhail Shkolnikov, IMI-BAS. Zoom link: https://us02web.zoom.us/j/83740034721?pwd=VnBtcVpGUktscHQ4a09jZkNZTURyZz09 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.

The next session of the Geometry Seminar of ICMS will be held on Wednesday, February 7, 2024, at 16:00, in room 403 and via Zoom. A talk on: Introduction to curve counting will be delivered by Mikhail Shkolnikov, IMI-BAS. Zoom link: https://us02web.zoom.us/j/83740034721?pwd=VnBtcVpGUktscHQ4a09jZkNZTURyZz09 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 [...]