# A(achen)-B(ochum)-C(ologne)-D(arstellungstheorie) Seminar

# Wintersemester 2021/22

### Organizer: Peter Littelmann, Xin Fang

## Speakers

George Balla (Aachen), Rocco Chirivì (Lecce), Aran Tattar (Cologne), Nick Williams (Cologne)## Schedule

The seminar will be held on**11, January, 2022**in the virtual space via zoom

https://uni-koeln.zoom.us/j/99397855430?pwd=QUxDM2M1aXZIR3FITk9vL0UzbVJmQT09

Meeting ID: 993 9785 5430

Password: 140997

### Schedule of talks:

14h-14h30 Nick Williams (Cologne): An algebraic interpretation of the higher Stasheff--Tamari orders

14h45-15h15 Aran Tattar (Cologne): Torsion structures, subobjects and unique filtrations in non-abelian categories

15h30-16h30 Rocco Chirivì (Lecce): Seshadri stratification and standard monomial theory

16h45-17h15 George Balla (Aachen): Tropical symplectic flag varieties: a Lie theoretic approach

## Abstract

#### Aran Tattar

Torsion structures, subobjects and unique filtrations in non-abelian categoriesThis is an overview of my PhD studies. I'll discuss torsion pairs for quasi-abelian categories, intersections & sums of subobjects in exact categories and the role of right triangulated categories in (co-)t-structures.

#### Rocco Chirivì

Seshadri stratification and standard monomial theoryI will introduce the notion of a Seshadri stratification on an embedded projective variety. Such a structure enables the construction of a Newton-Okounkov simplicial complex and a flat degeneration of the projective variety into a union of toric varieties. Moreover a Seshadri stratification provides a geometric setup for a standard monomial theory. In particular, the Lakshmibai-Seshadri paths for Schubert varieties get a geometric interpretation as successive vanishing orders of regular functions.

#### George Balla

Tropical symplectic flag varieties: a Lie theoretic approachI will describe a polyhedral cone given by certain degree functions on the root system of the symplectic Lie algebra. This cone interlaces tropical geometry of symplectic flag varieties with Lie theory. In this framework, one obtains a toric variety of the symplectic FFLV polytope. This is ongoing joint work with Xin Fang.

## Practical information

There is no registration needed.For further questions, please contact xfang@math.uni-koeln.de

Arbeitsgruppe Algebra und Zahlentheorie, Mathematisches Institut, Universität zu Köln