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SS 2025
09.04.2025 um 09:00 Uhr in 69/E15
Thiago Holleben (Dalhousie University Canada)
Coinvariant stresses, Lefschetz properties and random complexes
In 1996, Lee translated the notion of stress of bar and joint frameworks to the algebraic notion of inverse systems from commutative algebra. In this talk we apply this connection to introduce the notion of a coinvariant stress, and give a formula for the top coinvariant stress of spheres. We then apply these ideas to generalize a result of Migliore, Miró-Roig and Nagel on the Lefschetz properties of monomial almost complete intersections.
23.04.2025 um 09:00 Uhr in 69/117
Nicola da Ponte (SISSA)
Schubert calculus and the probabilistic intersection ring
I will first present the main ideas of the classical Schubert calculus in connection with enumerative geometry over the complex numbers. A real version of these ideas finds a natural setting in a probabilistic intersections ring, whose construction was recently proposed by Breiding, Bürgisser, Lerario, and Mathis. I will then introduce this probabilistic intersection ring and discuss Schubert calculus in this context.e study scattering equations of hyperplane arrangements from the perspective of combinatorial commutat
30.04.2025 um 09:00 Uhr in 69/117
Sarah Eggleston (Universität Osnabrück)
Real subrank of order- three tensors
We study the subrank of real order-three tensors and give an upper bound to the subrank of a real tensor given its complex subrank. For several small tensor formats, we investigate the typical subranks. Finally, we consider the tensor associated to componentwise complex multiplication in C^n and show that this tensor has real subrank n - informally, no more than n real scalar multiplications can be carried out using a device that does n complex scalar multiplications.
07.05.2025 um 09:00 Uhr in 69/117
Jhon Bladimir Caicedo Portilla (Universität Osnabrück)
Unimodular Triangulations and Ehrhart-Negativity for s-Lecture Hall Simplices
Given a sequence of positive integers s = (s_1, ..., s_n), the s-lecture hall simplex is defined as P_n^s = conv{(0, ..., 0), (0, ..., s_n), ..., (s_1, ..., s_n)}. It has been conjectured that for any sequence s, P_n^s admits a unimodular triangulation (UT). In this work, we provide new evidence for this conjecture by proving that if P_n^s admits a UT, then so does P_n^{s'}, where s'=(s_1,...,s_n+1). Additionally, given s = (a, ..., a, a+1)\in \Z^{n} with a\in\Z^+ and n > 4, we show that P_n^s is not Ehrhart positive for sufficiently large a. This is joint work with Martina Juhnke and Germain Poullot.
14.05.2025 um 09:00 Uhr in 69/117
Lakshmi Ramesh (Universität Bielefeld)
Convex Bodies and Maximum Likelihood Sets
We consider points sampled from a uniform distribution on a convex body in high dimensional real space with unknown location. In this case, the maximum likelihood estimator set is a convex body
containing the true location parameter, and hence has a volume and diameter. We estimate these quantities, in terms of dimension and number of samples, by introducing upper and lower bounds. These bounds are
different depending on the geometry of the convex body. We arrive at our results by employing algebraic, probabilistic and statistical techniques.
