Geometry Seminar of ICMS

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  

2024-03-26T10:20:39+02:00Tuesday, 26 March 2024|Categories: |Tags: , |

Geometry Seminar of ICMS

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 [...]

2024-03-15T10:05:57+02:00Friday, 15 March 2024|Categories: |Tags: , |

ICMS Seminar

Time: March 14, 2024, 2:00 pm Place: Room 403, IMI - BAS Speaker: Morgan Brown  (University of Miami) Title: Cox rings and characterization of toric varieties Further information: https://icms.bg/the-cox-ring-perspective-in-birational-geometry-talk-by-morgan-brown/ Abstract. Recently Moraga and Svaldi proved a conjecture of Shokoruv, characterizing in the relative case toroidal morphisms as those which admit divisors with many components relative to the Picard rank. I will discuss the global version, proved in previous joint work with McKernan, Svaldi and Zong. The proof relies on characterizing the singularity type of the Cox ring, giving another example of the use of these invariants in birational geometry.

2024-03-12T01:06:30+02:00Tuesday, 12 March 2024|Categories: |Tags: |

ICMS Seminar

Time: March 12, 2024, 2:00 pm Place: Room 403, IMI - BAS Speaker: Morgan Brown  (University of Miami) Title: The Cox ring perspective on birational geometry Further information: https://icms.bg/the-cox-ring-perspective-in-birational-geometry-talk-by-morgan-brown/ Abstract. The Mori program for birational classification of algebraic varieties attempts to classify algebraic varieties by producing canonical models, polarized by the canonical class. This is accomplished through a series of algebraic surgery operations, such as flips, flops, and divisorial contractions. A complementary viewpoint is that of the total coordinate ring or Cox ring. Here birational maps are understood by looking at the totality of all linear series on the variety, endowed with a ring structure directly analogous to that of the homogeneous coordinate ring of a projective variety. I will give an overview of [...]

2024-03-12T01:01:38+02:00Tuesday, 12 March 2024|Categories: |Tags: |

Geometry Seminar of ICMS

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 [...]

2024-02-22T11:19:16+02:00Thursday, 22 February 2024|Categories: |Tags: , |

Geometry Seminar of ICMS

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.

2024-02-12T15:39:25+02:00Monday, 12 February 2024|Categories: |Tags: , |

ICMS Seminar

Time: February 13, 2024, 2:00 pm Place: Room 403, IMI - BAS Speaker: Jean-Pierre Gazeau (APC, Université Paris - Cité) Title: Quantum circuit complexity for light polarisation or complexity with no complex numbers Further information: https://icms.bg/quantum-circuit-complexity-for-light-polarisation-or-complexity-with-no-complex-number-talk-by-jean-pierre-gazeau/ Abstract. 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 approach involves the analysis of sequences of density matrices. Each density matrix evolves within the framework of a Gorini-Kossakowski-Lindblad-Sudarshan (GKLS) process during the time interval between consecutive gates. Notably, when [...]

2024-02-09T11:45:25+02:00Friday, 9 February 2024|Categories: |Tags: |

Geometry Seminar of ICMS

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 [...]

2024-02-05T23:20:38+02:00Monday, 5 February 2024|Categories: |Tags: , |

ICMS Seminar

Time: February 8, 2024, 2:00 pm Place: Room 403, IMI - BAS Speaker: Vladimir Mitankin, IMI - BAS Title: A categorical view of singularity theory II Further information: https://icms.bg/a-categorical-view-of-singularity-theory-i-and-ii-talks-by-paul-horja/ Abstract. 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 [...]

2024-02-05T23:20:26+02:00Monday, 5 February 2024|Categories: |Tags: |

Geometry Seminar of ICMS

The next session of the Geometry Seminar of ICMS will be held on Wednesday, January 24, 2024, at 16:00, in room 403 and via Zoom. A talk on: Derived Deformation Theory and Formal Moduli Problem will be delivered by Yingdi Qin, IMI-BAS. Zoom link: https://us02web.zoom.us/j/83740034721?pwd=VnBtcVpGUktscHQ4a09jZkNZTURyZz09 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, [...]

2024-01-31T17:05:15+02:00Tuesday, 30 January 2024|Categories: |Tags: , |
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