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Abstracts for Algebra Seminar

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Classification of Disconnected Reductive Algebraic Groups

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Speaker: 
Dylan Johnston
Affiliation: 
Warwick
Date: 
Wed, 12/02/2025 - 11:00 - 12:00
Location: 
MPIM Seminar Room
Parent event: 
Algebra Seminar
Details: 
Program and Abstracts of Classification of Disconnected Reductive Algebraic Groups

We say a disconnected algebraic group is reductive if its connected component is a reductive group in the usual sense. Even if one is only interested in connected reductive groups, disconnected ones enter the picture as subgroups, so gaining an understanding of them is a fruitful endeavour. In this talk, I will discuss the following question: Given a connected reductive algebraic group N and a finite group H, which algebraic groups G fit into the short exact sequence 1 --> N --> G --> H --> 1?

Knutson's Conjecture on the Representation Ring

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Speaker: 
Diego Martin Duro
Affiliation: 
Warwick
Date: 
Wed, 19/02/2025 - 11:00 - 12:00
Location: 
MPIM Seminar Room
Parent event: 
Algebra Seminar

Donald Knutson’s Conjecture, later refined by Savitskii, stated that for every irreducible character of a finite group, there exists a virtual character such that their tensor product results in the regular character. The original conjecture was disproven by Savitskii, and we revisit the arguments and counterexamples provided.

Density functions for filtrations of homogeneous ideals

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Speaker: 
Hoang Le Truong
Affiliation: 
Vietnam Academy of Science and Technology
Date: 
Tue, 25/02/2025 - 14:00 - 15:30
Location: 
MPIM Seminar Room
Parent event: 
Algebra Seminar

A density function for an algebraic invariant is a measurable function on $\mathbb{R}$ that evaluates the invariant on a real scale. This approach encapsulates richer information about the invariant without requiring additional data. In this talk, we introduce and develop density functions $f_{I_n}$ corresponding to filtrations $\left\{I_n\right\}_{n \in \mathbb{N}}$ of graded ideals within a standard graded domain $A$. This is joint work with Suprajo Das and Sudeshna Roy.

Syzygies of the residue field over a local ring

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Speaker: 
Toshinori Kobayashi
Affiliation: 
Meiji University
Date: 
Tue, 04/03/2025 - 14:00 - 15:30
Location: 
MPIM Seminar Room
Parent event: 
Algebra Seminar

The syzygies of the residue field over a commutative local ring are important invariants of the ring. However, their module structure remains largely unexplored. In this talk, I'll discuss our results, focusing on the direct summands of the syzygies of the residue field. The talk consists of two parts.

 

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