tbranzov

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So far tbranzov has created 110 blog entries.
8 04, 2024

Reading seminar of geometric Lubin-Tate theory, by Jiachang Xu – part III

2024-04-08T22:35:15+03:00April 8th, 2024|Geometry Seminar|

In the last few decades, Berkovich’s theory of k -analytic space has extended classic rigid geometry. Since k -analytic space has good topological properties, and the Berkovich analytification of algebraic varieties could be also dealt with via the geometry of the model and it has a strong connection with tropical geometry, this allows us to use the combinatorial techniques to study algebraic varieties. Our lectures will mainly discuss the contents of Berkovich space and its application in other aspects of mathematics, we plan to go over the basic properties of Berkovich space in both algebraic and topological ways for the first lecture. 

31 03, 2024

Reading seminar of geometric Lubin-Tate theory, by Jiachang Xu – part II

2024-03-31T12:10:49+03:00March 31st, 2024|Geometry Seminar|

In the last few decades, Berkovich’s theory of k -analytic space has extended classic rigid geometry. Since k -analytic space has good topological properties, and the Berkovich analytification of algebraic varieties could be also dealt with via the geometry of the model and it has a strong connection with tropical geometry, this allows us to use the combinatorial techniques to study algebraic varieties. Our lectures will mainly discuss the contents of Berkovich space and its application in other aspects of mathematics, we plan to go over the basic properties of Berkovich space in both algebraic and topological ways for the first lecture. 

25 03, 2024

Reading seminar of geometric Lubin-Tate theory, by Jiachang Xu – part I

2024-03-31T12:10:27+03:00March 25th, 2024|Geometry Seminar|

In the last few decades, Berkovich’s theory of k -analytic space has extended classic rigid geometry. Since k -analytic space has good topological properties, and the Berkovich analytification of algebraic varieties could be also dealt with via the geometry of the model and it has a strong connection with tropical geometry, this allows us to use the combinatorial techniques to study algebraic varieties. Our lectures will mainly discuss the contents of Berkovich space and its application in other aspects of mathematics, we plan to go over the basic properties of Berkovich space in both algebraic and topological ways for the first lecture. 

13 03, 2024

Ellipsoid superpotentials: obstructing symplectic embeddings by singular algebraic curves, a talk by Grigory Mikhalkin

2024-03-13T14:20:00+02:00March 13th, 2024|Geometry Seminar, News|

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...

11 03, 2024

Dynamical zeta function for billiard flow, colloquium talk by Vesselin Petkov

2024-03-11T15:19:53+02:00March 11th, 2024|Colloquium, News|

Vesselin Petkov is a professor emeritus ат the University of Bordeaux who has made important contributions to hyperbolic partial differential equations, spectral and scattering theory and dynamical systems.

20 02, 2024

Linear embeddings of complex Grassmannians, a talk by Ivan Penkov

2024-02-20T11:00:10+02:00February 20th, 2024|Geometry Seminar|

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.

12 02, 2024

Refined curve counting, a talk by Mikhail Shkolnikov

2024-02-12T09:51:35+02:00February 12th, 2024|Geometry Seminar|

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.

8 02, 2024

Quantum circuit complexity for light polarisation or complexity with no complex number, talk by Jean-Pierre Gazeau

2024-02-12T09:43:47+02:00February 8th, 2024|ICMS Seminar, News|

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.

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