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|Speaker||Title||Date & Time||Duration||Zoom||Abstract||Seminar|
|Donghyun Kim||A combinatorial formula for the coefficients of the Al-Salam-Chihara polynomials||Mon 30 Mar 2020 19:10 UTC||50 minutes||https://berkeley.zoom.us/s/8807500210||Show||6|
|Kathlén Kohn (KTH Royal Institute of Technology, Stockholm)||Minimal Problems in Computer Vision||Tue 31 Mar 2020 15:00 UTC||30 minutes||No Zoom link - View Seminar page||Show||3|
|Mima Stanojkovski (MPI MIS, Leipzig)||Toric varieties from cyclic matrix groups||Tue 31 Mar 2020 15:40 UTC||30 minutes||No Zoom link - View Seminar page||Show||3|
|Valeria Bertini (Technical University Chemnitz)||Hyperkähler manifolds and rational curves||Tue 31 Mar 2020 16:20 UTC||30 minutes||No Zoom link - View Seminar page||Show||3|
|Alexander Heaton (Max Planck Institute)||Epsilon local rigidity and numerical algebraic geometry||Thu 02 Apr 2020 14:00 UTC||Check Seminar Page||https://mit.zoom.us/j/481638076||Show||2|
|Tomack Gilmore (University College London)||Plane partitions, rhombus tilings, lattice paths, and perfect matchings (with some pretty pictures)||Thu 02 Apr 2020 14:00 UTC||45 minutes||email Ulrich Pennig (firstname.lastname@example.org)||Show||1|
|Roser Homs Pons (MPI MIS, Leipzig)||Primary ideals and their differential equations||Thu 02 Apr 2020 15:00 UTC||30 minutes||No Zoom link - View Seminar page||Show||3|
|Miruna-Stefana Sorea (MPI MIS, Leipzig)||Exact Solutions in Log-Concave Maximum Likelihood Estimation||Thu 02 Apr 2020 15:40 UTC||30 minutes||No Zoom link - View Seminar page||Show||3|
|Türkü Özlüm Celik (University of Leipzig)||Lie’s double translation surfaces meet theta surfaces||Thu 02 Apr 2020 16:20 UTC||30 minutes||No Zoom link - View Seminar page||Show||3|
|Brendan Pawlowski||The fraction of an S_n-orbit on a hyperplane||Mon 06 Apr 2020 19:10 UTC||50 minutes||https://berkeley.zoom.us/s/8807500210||Show||6|
|Amzi Jeffs (University of Washington)||TBA||Mon 06 Apr 2020 20:10 UTC||50 minutes||https://ucdavisdss.zoom.us/j/842986080||No abstract available||7|
|Ben Hollering (North Carolina State University)||Identifiability in Phylogenetics using Algebraic Matroids||Tue 07 Apr 2020 14:00 UTC||Check Seminar Page||https://mit.zoom.us/j/481638076||Show||2|
|Alexander Ruys de Perez (Texas A&M University)||TBA||Wed 08 Apr 2020 22:30 UTC||90 minutes||https://washington.zoom.us/j/119060044||No abstract available||10|
|1||Geometry, Algebra, Mathematical Physics and Topology Research Group||Cardiff Univesity||Seminar Website|
|2||Virtual seminar on algebraic matroids and rigidity theory||MIT||Seminar Website|
|3||Nonlinear Algebra Seminar Online||Max-Planck-Instut für Mathematik (MPI)||Seminar Website|
|4||Combinatorics Lectures Online||Princeton University||Seminar Website|
|5||Workshop on combinatorics, discrete geometry and algorithms||St. Petersburg State University||Seminar Website|
|6||Combinatorics Seminar||UC Berkeley||Seminar Website|
|7||Algebra and Discrete Mathematics Seminar||UC Davis||Seminar Website|
|8||Discrete Math Seminar||University of Massachusetts Amherst||Seminar Website|
|9||Combinatorics Seminar||University of Minnesota||Seminar Website|
|10||Combinatorics and Geometry Seminar||University of Washington||Seminar Website|
|11||WinCom Virtual Colloquium||Women in Combinatorics||Seminar Website|
|12||Applied Algebra Seminar||York University||Seminar Website|
The Al-Salam-Chihara polynomials are an important family of orthogonal polynomials in one variable x depending on 3 parameters alpha, beta and q. They are closely connected to a model from statistical mechanics called the partially asymmetric simple exclusion process (PASEP). We give a combinatorial formula for the coefficients of the (transformed) Al-Salam-Chihara polynomials and discuss the positivity phenomenon.Close
A well-studied problem in computer vision is “”structure from motion“”, where 3D structures and camera poses are reconstructed from given 2D images taken by the unknown cameras. The most classical instance is the 5-point problem: given 2 images of 5 points, the 3D coordinates of the points and the 2 camera poses can be reconstructed. In fact, given 2 generic images of 5 points, this problem has 20 solutions (i.e., 3D coordinates + 2 camera poses) over the complex numbers. Reconstruction problems which have a finite positive number of solutions given generic input images, such as the 5-point problem, are called “”minimal“”. These are the most relevant problem instances for practical algorithms, in particular those with a small generic number of solutions. We formally define minimal problems from the point of view of algebraic geometry. Our algebraic techniques lead to a classification of all minimal problems for point-line arrangements completely observed by any number of cameras. We compute their generic number of solutions with symbolic and numerical methods. This is joint work with Timothy Duff, Anton Leykin, and Tomas Pajdla.Close
We discuss algebro-geometric properties of the Zariski closure of cyclic matrix groups or semigroups. We will go through several examples and through an implementation in SageMath. This is joint work with Francesco Galuppi.Close
I will introduce Hyperkähler manifolds, a class of manifolds very much studied in complex algebraic geometry; they can be thought as a higher dimensional alanogue of K3 surfaces. I will present a geometrical problem on them, that is the existence of rational curves, i.e. curves birational to a projective line; the problem has a complete solution in the case of K3 surfaces, but much less is known in the Hyperkähler case.Close
A well-known combinatorial algorithm can decide generic rigidity in the plane by determining if the graph is of Pollaczek-Geiringer-Laman type. Methods from matroid theory have been used to prove other interesting results, again under the assumption of generic configurations. However, configurations arising in applications may not be generic. We present Theorem 7 and its corresponding Algorithm 1 which decide if a configuration is epsilon-locally rigid, a notion we define. This provides a partial answer to a problem discussed in the 2011 paper of Hauenstein, Sommese, and Wampler. We also use numerical algebraic geometry to find nearby valid configurations which are not obtained by rigid motions. This is joint work with Andrew Frohmader.Close
Plane partitions were first studied by Gen. Percy Alexander MacMahon at the beginning of the twentieth century and since then these objects have been studied by mathematicians and mathematical physicists alike.Close
An ideal in a polynomial ring encodes a system of linear partial differential equations with constant coefficients. Primary decomposition organizes the solutions to the PDE. The primary ideals arising in such a decomposition can be characterized in terms of certain differential equations. In this talk we will understand how this characterization works. We will give an explicit algorithm for computing these differential operators that describe a primary ideal, namely Noetherian operators. For some special cases, we will give an alternative representation of the primary ideal by differential equations playing with the join construction. This is a joint work with Yairon Cid-Ruiz and Bernd Sturmfels.Close
We study probability density functions that are log-concave. Despite the space of all such densities being infinite-dimensional, the maximum likelihood estimate is the exponential of a piecewise linear function determined by finitely many quantities, namely the function values, or heights, at the data points. We explore in what sense exact solutions to this problem are possible. Joint work with Alexandros Grosdos, Alexander Heaton, Kaie Kubjas, Olga Kuznetsova, and Georgy Scholten.Close
A theta surface in affine 3-space is the zero set of a Riemann theta function. This includes surfaces arising from special plane quartics that are singular or reducible. Lie and Poincaré showed that theta surfaces are precisely the surfaces of double translation, i.e. obtained as the Minkowski sum of two space curves in two different ways. These curves are parametrized by abelian integrals, so they are usually not algebraic. This is joint work with Daniele Agostini, Julia Struwe and Bernd Sturmfels which offers a new view on this classical topic through the lens of computation.Close
Huang, McKinnon, and Satriano conjectured that if a real
vector (v_1, ..., v_n) has distinct coordinates and n ≥ 3, then a
hyperplane through the origin other than x_1 + ... + x_n = 0 contains
at most 2(n−2)!floor(n/2) of the vectors obtained by permuting the
coordinates of v. I will discuss a proof of this conjecture.
Identifiability is a crucial property for a statistical model since it implies that distributions in the model uniquely determine the parameters that produce them. In phylogenetics, the identifiability of the tree parameter is of particular interest since it means that phylogenetic models can be used to infer evolutionary histories from data. Typical strategies for proving identifiability results require Gröbner basis computations which become untenable as the size of the model grows. In this talk I'll give some background on phylogenetic algebraic geometry and then discuss a new computational strategy for proving the identifiability of discrete parameters in algebraic statistical models that uses algebraic matroids naturally associated to the models. This algorithm allows us to avoid computing Gröbner bases and is also parallelizable.Close