# Abstracts for Algebra, Geometry and Physics: a mathematical mosaic

Alternatively have a look at the program.

## Fibonacci structures related to adjoint functors and semi-orthogonal decompositions

Posted in
Speaker:
Mikhail Kapranov
Affiliation:
Kavli IPMU
Date:
Tue, 08/03/2022 - 11:00 - 12:00

Various contractions of the composition of a string of iterated adjoint functors form
a diagram whose shape is known in computer science as the "Fibonacci cube".
Such diagrams can be seen as categorical lifts of Euler continuants, the universal numerators
and denominators of finite continued fractions whose entries are independent variables.
Vanishing (exactness) of the totalization of the (N-1)st Fibonacci cube defines the concept
of an N-spherical functor, with usual spherical functors appearing

## Categorical dynamics: from Hopfield to Pareto

Posted in
Speaker:
Matilde Marcolli
Affiliation:
Caltech
Date:
Tue, 08/03/2022 - 13:45 - 15:30

This talk is part of the Algebra, Geometry and Physics Seminar (MPIM/HU Berlin), host Gaetan Borot,
contact: gaetan.borot@hu-berlin.de

## Algebra, Geometry and Physics: From Feynman graphs to moduli spaces

Posted in
Speaker:
Ralph Kaufmann
Affiliation:
Purdue University
Date:
Tue, 08/03/2022 - 16:00 - 17:00

We present a program which is designed to take combinatorial categorical data and produce geometric spaces
and classify universal algebraic operations. Specifically when applied to categories of graphs as founded by Borisov-Manin thought of as Feynman graphs, this program on one hand produces cubical and simplicial complexes corresponding to moduli spaces of Riemann surfaces and their Kontsevich-Penner compactifications.

## A brief visit to flag country: reminiscences and recent results

Posted in
Speaker:
Ivan Penkov
Affiliation:
Jacobs University Bremen
Date:
Wed, 09/03/2022 - 11:00 - 12:00

## Non-isogenous elliptic curves and hyperelliptic jacobians

Posted in
Speaker:
Yuri Zarhin
Affiliation:
Penn State/MPIM
Date:
Wed, 09/03/2022 - 14:30 - 15:30

Let $E_f: y^2=f(x)$ and $E_h: y^2=h(x)$ be elliptic curves over a field
$K$ of characteristic zero that are defined by cubic polynomials
$f(x)$ and $h(x)$ with coefficients in $K$.

Suppose that one of the polynomials is irreducible and the other
reducible.
We prove that if $E_f$ and $E_h$ are isogenous over an algebraic closure
$\bar{K}$ of $K,$ then they both are isogenous
to the elliptic curve $y^2=x^3-1$ over $\bar{K}$.

## A non-commutative view of Fano threefolds

Posted in
Speaker:
Arend Bayer
Affiliation:
University of Edinburgh
Date:
Thu, 10/03/2022 - 13:30 - 14:30

The classification of Fano threefolds of Picard rank one gains more structure when instead of varieties, we consider a natural subcategory of its derived category, now called Kuznetsov component.
I will give an overview of recent results about, and based on, these Kuznetsov components. The methods involve moduli spaces of Bridgeland-stable objects, and equivariant categories.

## Blow-up formula for quantum cohomology

Posted in
Speaker:
Maxim Kontsevich
Affiliation:
IHES
Date:
Thu, 10/03/2022 - 15:00 - 16:00

Yu. I. Manin greatly contributed to several areas of algebraic
geometry, in particular to questions of rationality, and to quantum
cohomology. I will speak about an application of the latter to the
former: the very general cubic fourfold is not rational. The main
ingredient is a blow up formula for genus 0 Gromov-Witten invariants
(the proof is expected soon). Another output is a definition of
"correct" cohomology and GW invariants for singular varieties.

## Geometric methods in representation theory of supergroups

Posted in
Speaker:
Vera Serganova
Affiliation:
University of California, Berkeley
Date:
Thu, 10/03/2022 - 16:30 - 17:30

We will discuss several approaches to the support varieties for the
categories of rational representations of algebraic supergroups with reductive
underlying groups. In particular, we explain how our support theory is related to
geometric properties of supergrassmannians and Deligne categories.

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