15.10.2019 um 16:15 Uhr in 69/125:
Mandira Mondal (Chennai Mathematical Institute, India)
Density function for the second coefficient of the Hilbert-Kunz function on projective toric varieties
05.11.2019 um 16:15 Uhr in 69/125:
Ilya Smirnov (Stockholm University)
Improving Lech's inequality
Lech's inequality is a fundamental inequality in a local ring that uniformly relates the multiplicity and the colength of a finite colength ideal. For monomial ideals there is a nice combinatorial proof and the general proof reduces to this case. Lech's inequality is never sharp in dimension at least two and in my talk I will present a way to fix it.
12.11.2019 um 16:15 Uhr in 69/125:
Yairon Cid Ruiz (MPI Leipzig)
Noetherian operators, primary submodules and symbolic powers
We give an algebraic and self-contained proof of the existence of the so-called Noetherian operators for primary submodules over general classes of Noetherian commutative rings. The existence of Noetherian operators accounts to provide an equivalent description of primary submodules in terms of differential operators. As a consequence, we introduce a new notion of differential powers which coincides with symbolic powers in many interesting non-smooth settings, and so it could serve as a generalization of the Zariski-Nagata Theorem.
19.11.2019 um 16:15 Uhr in 69/125:
Andrew Newman (TU Berlin)
Enumerating simplicial complexes up to homotopy equivalence
The Dedekind numbers enumerate labeled simplicial complexes on n vertices and grow at a rate which is doubly exponential in n. Here we show that such a rate of growth also holds for simplicial complexes on n vertices even enumerating only up to homotopy equivalence. This is accomplished by exhibiting many possible homology groups which are realizable by simplicial complexes on n vertices. This is direction of research is motivated by surprising properties observed in homology of random complexes and the proof relies on the probabilistic method.
19.11.2019 um 17:15 Uhr in 69/125:
Mitra Koley (Chennai Mathematical Institute, India)
Hilbert-Kunz functions and Hilbert-Kunz multiplicities of Rees algebras
First we define Hilbert-Kunz functions and Hilbert-Kunz multiplicity of a local/graded ring. Then we discuss Hilbert-Kunz functions and Hilbert-Kunz multiplicities of Rees algebras. This is joint work with J.K. Verma and K. Goel.
26.11.2019 um 16:15 Uhr in 69/125:
Joseph Samuel Doolittle (FU Berlin)
Relative Complexes as a Construction Tool
Many properties defined for simplicial complexes allow an equivalent definition for relative complexes. Cohen-MaCaulay, shellability, partitonability, and homology have fundamentally equivalent definitions for both simplicial and relative complexes. We take advantage of this to find relative complexes with interesting properties that would be intensely challenging to find directly in simplicial complexes. Then through repeated gluing, we can construct simplicial complexes with our desired interesting properties. This technique which was first used to great effect by Duval, Goeckner, Klivans, and Martin in 2016. We will illustrate the technique with two recent results in joint work with Goeckner and Lazar.
26.11.2019 um 17:15 Uhr in 69/125:
Ulrich von der Ohe (Università degli Studi di Genova, Italy)
Algebraic decomposition of functions from evaluations
The task of decomposing certain functions in terms of given vector space bases is historically motivated by physics and recently finds applications in signal and image processing. Prony's work from 1795 remains central to this subject. In this talk, we discuss instances and variations of this problem, their Prony structures and relations. The talk is based on recent joint work with Stefan Kunis and Tim Römer.
28.11.2019 um 16:15 Uhr in 69/125:
Bogdan Ichim (University of Bucharest, Romania)
On a class of Gorenstein polytopes
We present a new class of Gorenstein polytopes, which was found by experimental computations with Normaliz.