Seminars and Colloquia by Series

Patchworking oriented matroids

Series
Algebra Seminar
Time
Wednesday, October 28, 2020 - 15:30 for 1 hour (actually 50 minutes)
Location
https://bluejeans.com/751242993/PASSWORD (To receive the password, please email Lutz Warnke)
Speaker
Marcel CelayaTU Berlin

A classical result on oriented matroids due to Folkman and Lawrence in
1978 states that they are in bijection with pseudosphere arrangements up
to cellular homeomorphism. A more recent result, conjectured by Ardila and
Develin in 2007 and proved by Silke Horn in 2016, states that a similar
result holds for tropical oriented matroids and tropical hyperplane
arrangements. In a joint work with Georg Loho and Chi Ho Yuen, we show how
to unify these two results based on a variant of Viro's patchworking
technique, generalized to complete intersections by Sturmfels, for a
certain class of uniform oriented matroids arising from a product of two
simplices.

TBA by Éva Czabarka

Series
Graph Theory Seminar
Time
Tuesday, October 27, 2020 - 15:45 for 1 hour (actually 50 minutes)
Location
https://us04web.zoom.us/j/77238664391. For password, please email Anton Bernshteyn (bahtoh ~at~ gatech.edu)
Speaker
Éva CzabarkaUniversity of South Carolina

TBA

Two results on the interaction energy

Series
Analysis Seminar
Time
Tuesday, October 27, 2020 - 14:00 for 1 hour (actually 50 minutes)
Location
https://us02web.zoom.us/j/71579248210?pwd=d2VPck1CbjltZStURWRWUUgwTFVLZz09
Speaker
Yao YaoGeorgia Tech


For any nonnegative density f and radially decreasing interaction potential W, the celebrated Riesz rearrangement inequality shows the interaction energy E[f] = \int f(x)f(y)W(x-y) dxdy satisfies E[f] <= E[f^*], where f^* is the radially decreasing rearrangement of f. It is a natural question to look for a quantitative version of this inequality: if its two sides almost agree, how close must f be to a translation of f^*? Previously the stability estimate was only known for characteristic functions. I will discuss a recent work with Xukai Yan, where we found a simple proof of stability estimates for general densities. 

I will also discuss another work with Matias Delgadino and Xukai Yan, where we constructed an interpolation curve between any two radially decreasing densities with the same mass, and show that the interaction energy is convex along this interpolation. As an application, this leads to uniqueness of steady states in aggregation-diffusion equations with any attractive interaction potential for diffusion power m>=2, where the threshold is sharp.

Oriented Matroids from Triangulations of Products of Simplices

Series
Combinatorics Seminar
Time
Friday, October 23, 2020 - 15:00 for 1 hour (actually 50 minutes)
Location
https://bluejeans.com/751242993/PASSWORD (To receive the password, please email Lutz Warnke)
Speaker
Chi Ho YuenBrown University

We introduce a construction of oriented matroids from any triangulation of a product of two simplices, extending the regular case which follows from signed tropicalization. For this, we use the structure of such a triangulation in terms of polyhedral matching fields. The oriented matroid is composed of compatible chirotopes on the cells in a matroid subdivision of the hypersimplex, which might be of independent interest. We will also describe the extension to matroids over hyperfields and sketch some connections with optimization. This is joint work with Marcel Celaya and Georg Loho; Marcel Celaya will be giving a talk on the topological aspect of the work at the algebra seminar next week.

Alice in Königsberg

Series
Other Talks
Time
Thursday, October 22, 2020 - 20:00 for 30 minutes
Location
ONLINE at https://zoom.us/j/93502013825
Speaker
Evans Harrell and GT Club Math studentsGeorgia Tech

This skit recounts one of the foundation stories of mathematics, the puzzle of the Seven Bridges of Königsberg, solved by Euler in 1726.  Except that it all takes place in a mad courtroom, and you are the jury!

Higher-order fluctuations in dense random graph models (note the unusual time/day)

Series
Combinatorics Seminar
Time
Thursday, October 22, 2020 - 17:00 for 1 hour (actually 50 minutes)
Location
https://bluejeans.com/751242993/PASSWORD (To receive the password, please email Lutz Warnke)
Speaker
Adrian RoellinNational University of Singapore

Dense graph limit theory is essentially a first-order limit theory analogous to the classical Law of Large Numbers. Is there a corresponding central limit theorem? We believe so. Using the language of Gaussian Hilbert Spaces and the comprehensive theory of generalised U-statistics developed by Svante Janson in the 90s, we identify a collection of Gaussian measures (aka white noise processes) that describes the fluctuations of all orders of magnitude for a broad family of random graphs. We complement the theory with error bounds using a new variant of Stein’s method for multivariate normal approximation, which allows us to also generalise Janson’s theory in some important aspects. This is joint work with Gursharn Kaur.

Please note the unusual time/day.

Higher-order fluctuations in dense random graph models (note the unusual time: 5pm)

Series
Stochastics Seminar
Time
Thursday, October 22, 2020 - 17:00 for 1 hour (actually 50 minutes)
Location
https://bluejeans.com/751242993/PASSWORD (To receive the password, please email Lutz Warnke)
Speaker
Adrian RoellinNational University of Singapore

Dense graph limit theory is essentially a first-order limit theory analogous to the classical Law of Large Numbers. Is there a corresponding central limit theorem? We believe so. Using the language of Gaussian Hilbert Spaces and the comprehensive theory of generalised U-statistics developed by Svante Janson in the 90s, we identify a collection of Gaussian measures (aka white noise processes) that describes the fluctuations of all orders of magnitude for a broad family of random graphs. We complement the theory with error bounds using a new variant of Stein’s method for multivariate normal approximation, which allows us to also generalise Janson’s theory in some important aspects. This is joint work with Gursharn Kaur.

Please note the unusual time: 5pm

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