The 12th of May is the International Women in Mathematics. We would like to invite all members of the TRR to a day of talks in Paderborn. All talk will be held in D2.314. Below you can find the speakers, the schedule, and titles and abstracts.
| Time | Speaker |
|---|---|
| 10.00 - 10.45 | Viktória Klász |
| 10.45 - 11.15 | Coffee break |
| 11.15 - 12.00 | Irene Garnelo Abellanas |
| 12.00 - 14.00 | Lunch break |
| 14.00 - 14.45 | Efthymia Papageorgiou |
| 14.45 - 15.15 | Coffee break |
| 15.15 - 16.00 | Ana Maria Botero |
Viktória Klász - Auslander regular algebras and Coxeter matrices
Auslander regular algebras were introduced by Auslander as non-commutative
analogues of the classical regular rings from commutative algebra. In this talk,
we will investigate how this homological condition for an algebra relates to
matrix factorisation properties of its Coxeter matrix. This gives us a linear
algebraic interpretation of the (homological) Auslander-Reiten bijection.
These relations turn out to be especially well-behaved for the class of inci-
dence algebras of lattices: Here we get a full classification of Auslander regularity
using the Coxeter matrices. Looking at this class, we can also discover how Aus-
lander regularity and related homological objects translate to lattice-theoretic
notions. As a corollary, we obtain a new, linear algebraic characterisation of
distributivity for finite lattices.
This talk is based on the paper: arxiv.org/abs/2501.09447
Irene Garnelo Abellanas - An introduction to the interactive theorem prover Lean
In recent years, interactive theorem provers have gained prominence as powerful tools for formalizing mathematics and verifying the correctness of proofs. A prime example is Fields-medallist Peter Scholze, who had one of his proofs in the field of condensed mathematics formalized by the theorem prover community. The talk will give an accessible introduction to the interactive theorem prover Lean and potential applications in research and education. If you bring a digital device you will be able to code along.
Efthymia Papageorgiou - Large sets containing no copies of a given infinite sequence
A “large scale” analogue of the Erdős similarity problem can be stated as follows: let A be a discrete, unbounded, infinite set in R; can we find a “large” measurable set E ⊂ R which
does not contain any affine copy x+tA of A (for any x ∈ R, t > 0)?
If an is a real, nonnegative sequence that does not increase exponentially, then, for any 0 ≤ p < 1, we construct a Lebesgue
measurable set which has measure at least p in any unit interval
and which contains no affine copy of the given sequence. We generalize this to higher dimensions and also for some “non-linear”
copies of the sequence. Our method is probabilistic.
Ana Maria Botero - Arithmetic geometry of Toric varieties
The Bernštein-Kušnirenko-Khovanskii theorem (BKK theorem) states that
the number of isolated common zeros (counted with multiplicities) of a
family of Laurent polynomials is bounded above by the volume of its
Newton polytope. This shows how a geometric problem (counting the number
of solutions of a system of equations) can be translated into a
combinatorial one. This result can be stated in the realm of Toric
geometry, an area of mathematics which forms a bridge between algebraic
geometry and combinatorics. The aim of this talk is to introduce Toric
varieties and explain the dictionary allowing to translate
algebro-geometric properties of Toric varieties in terms of properties
of polytopes and fans. Finally, we will enlarge the dictionary to the
arithmetic setting and state an arithmetic BKK theorem.