9 10, 2023

Tropical structures in sandpile model, talk by Mikhail Shkolnikov, IMI-BAS

2023-10-23T14:25:56+03:00October 9th, 2023|Geometry Seminar, ICMS Seminar, News|

I will tell how tropical curves arise in the scaling limit of the sandpile model in the vicinity of the maximal stable state and explain two major consequences inspired by this fact. The first one is that there is a continuous model for self-organized criticality, the only known model of a kind, defined in the realm of tropical geometry. The second is that the totality of recurrent states in the original sandpile model, the sandpile group, approximates a continuous group, a tropical Abelian variety, which is functorial with respect to inclusions of domains, allowing to compute its scaling limit as a space of circle-valued harmonic functions on the whole lattice.

29 09, 2023

Invariant theory, homogeneous projective varieties, and momentum maps, course by Valdemar Tsanov

2023-10-23T13:30:17+03:00September 29th, 2023|ICMS Seminar, News|

After introducing the basic notions, I will derive some properties of momentum images related to fundamental forms and osculating varieties, as well as a lower bound on the minimal positive degree of a homogeneous invariant, derived using secant varieties. At the end I will present a class of homogeneous projective varieties, characterized by a special property of their secant varieties, where the relations between the above three concepts take a particularly pristine form.

29 09, 2023

Introduction to Projective Structures and Opers, course by Peter Dalakov

2023-10-23T13:27:22+03:00September 29th, 2023|ICMS Seminar, News|

A complex projective structure on a Riemann surface is determined by an atlas, whose transition functions are Moebius (fractional-linear) transformations. There are multiple   descriptions of these structures: as certain flat PGL_2-bundles, as Sturm-Liouville operators, as holomorphic connections on the (first) jet bundle of the dual of a theta-characteristic, etc. This mini-course is an introduction to the fundamentals of projective structures, accessible to students and non-specialists. We will also explore links to some classical geometric objects (such as quadratic differentials and Schwarzian derivatives), as well as some generalisations (G-opers) introduced by Beilinson and Drinfeld.

29 09, 2023

About a generalisation of Sylvester’s law of inertia, talk by Stéphanie Cupit-Foutou

2023-10-05T13:00:01+03:00September 29th, 2023|ICMS Seminar, News|

Sylvester’s law of inertia can be formulated in terms of group actions when considering real linear groups acting on real quadratic forms by base change. After reviewing this celebrated result from this perspective, I will give a generalisation of it in the setting of so-called spherical varieties (a class of complex varieties including flag varieties, toric varieties, symmetric spaces, etc.). This is a joint work with D. Timashev

11 08, 2023

Remarks on Hodge Polynomials for Certain Non-algebraic Complex Manifolds, by Ernesto Lupercio

2023-08-31T14:14:48+03:00August 11th, 2023|Consortium Distinguished Lecture Series, News|

This two talks explore Hodge polynomials and their properties, specifically focusing on non-Kähler complex manifolds. We investigate several families of such manifolds, including (Quasi) Hopf, (Quasi) Calabi-Eckmann, and LVM manifolds, alongside a class of definable complex manifolds that encompasses both algebraic varieties and the aforementioned special cases. Our main result establishes the preservation of the motivic nature of Hopf polynomials inside this broader context.

11 08, 2023

Borel-Weil Theorem and Laplace eigenfunctions on Riemannian symmetric spaces, by Gueo Grantcharov

2023-08-31T14:12:58+03:00August 11th, 2023|Consortium Distinguished Lecture Series, News|

In this talk I'll present a geometric relation between the Laplace-Beltrami spectra and eigenfunctions on compact Riemannian symmetric spaces and the Borel-Weil theory using ideas from symplectic geometry and geometric quantization.

9 08, 2023

Period mappings for anti-canonical pairs, by Phillip Griffiths

2023-08-11T14:26:11+03:00August 9th, 2023|Consortium Distinguished Lecture Series, News|

Anti-canonical pairs (Y, D) are logarithmic K3 surfaces. It is well known that they have a rich geometry. A recent result, whose proof was motivated by mirror-symmetry, establishes a conjecture by Looijenga giving conditions for smoothability of the cusp obtained by contracting D. A central ingredient in the proof is a global Torelli theorem using the mixed Hodge structure on H2(Y −D). In this talk we will formulate and sketch the proof of this result.

9 08, 2023

The generazed Calabi-Yau problem, by Vestislav Apostolov

2023-08-09T10:57:36+03:00August 9th, 2023|Consortium Distinguished Lecture Series, News|

I will describe an extension, proposed by Hitchin and Gualtieri, of the notion of a Calabi-Yau structure to generalized Kähler geometry. I will then discuss a conjectural classification of the generalized Kähler Calabi-Yau geometries, expressed in terms of Bogomolov-Beauville decomposition, and present a partial resolution.

27 06, 2023

Introduction to tensor triangular geometry

2023-06-27T10:49:08+03:00June 27th, 2023|ICMS Seminar, News|

In a series of four talks, I will try to give a brief introduction to the subject and look at examples and applications following the exposition of universality, functoriality and localization, and triangulated categories and localization. The main references on the subject are the tensor triangulated categories and the Balmer spectrum and some examples and applications.

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