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 [...]