Seminars and Colloquia by Series

Constructing minimally 3-connected graphs

Series
Graph Theory Seminar
Time
Tuesday, February 23, 2021 - 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
Sandra KinganBrooklyn College, CUNY

A 3-connected graph is minimally 3-connected if removal of any edge destroys 3-connectivity. We present an algorithm for constructing minimally 3-connected graphs based on the results in (Dawes, JCTB 40, 159-168, 1986) using two operations: adding an edge between non-adjacent vertices and splitting a vertex of degree at least 4. To test sets of vertices and edges for 3-compatibility, which depends on the cycles of the graph, we develop a method for obtaining the cycles of $G'$ from the cycles of $G$, where $G'$ is obtained from $G$ by one of the two operations above.  We eliminate isomorphic duplicates using certificates generated by McKay's isomorphism checker nauty. The algorithm consecutively constructs the non-isomorphic minimally 3-connected graphs with $n$ vertices and $m$ edges from the non-isomorphic minimally 3-connected graphs with $n-1$ vertices and $m-2$ edges, $n-1$ vertices and $m-3$ edges, and $n-2$ vertices and $m-3$ edges. In this talk I will focus primarily on the theorems behind the algorithm. This is joint work with Joao Costalonga and Robert Kingan.

Symplectic Geometry of Anosov Flows in Dimension 3 and Bi-Contact Topology

Series
CDSNS Colloquium
Time
Friday, February 19, 2021 - 13:00 for 1 hour (actually 50 minutes)
Location
Zoom (see add'l notes for link)
Speaker
Surena HozooriGeorgia Tech

Please Note: Join Zoom Meeting https://zoom.us/j/97732215148?pwd=Z0FBNXNFSy9mRUx3UVk4alE4MlRHdz09 Meeting ID: 977 3221 5148 Passcode: 801074 One tap mobile +19292056099,,97732215148#,,,,*801074# US (New York) +13017158592,,97732215148#,,,,*801074# US (Washington DC) Dial by your location +1 929 205 6099 US (New York) +1 301 715 8592 US (Washington DC) +1 312 626 6799 US (Chicago) +1 669 900 6833 US (San Jose) +1 253 215 8782 US (Tacoma) +1 346 248 7799 US (Houston) Meeting ID: 977 3221 5148 Passcode: 801074 Find your local number: https://zoom.us/u/aecn4pJKSi

We give a purely contact and symplectic geometric characterization of Anosov flows in dimension 3 and set up a framework to use tools from contact and symplectic geometry and topology in the study of questions about Anosov dynamics. If time permits, we will discuss a characterization of Anosovity based on Reeb flows and its consequences.

Fractional chromatic number of graphs of bounded maximum degree

Series
Graph Theory Seminar
Time
Tuesday, February 16, 2021 - 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
Zdeněk DvořákCharles University

By the well-known theorem of Brooks, every graph of maximum degree Δ ≥ 3 and clique number at most Δ has chromatic number at most Delta. It is natural to ask (and is the subject of a conjecture of Borodin and Kostochka) whether this bound can be improved for graphs of clique number at most Δ - 1. While there has been little progress on this conjecture, there is a number of interesting results on the analogous question for the fractional chromatic number. We will report on some of them, including a result by myself Bernard Lidický and Luke Postle that except for a finite number of counterexamples, every connected subcubic triangle-free graph has fractional chromatic number at most 11/4.

TBA by Khadim War

Series
CDSNS Colloquium
Time
Friday, February 12, 2021 - 13:00 for 1 hour (actually 50 minutes)
Location
Zoom (see add'l notes for link)
Speaker
Khadim WarIMPA

Please Note: Join Zoom Meeting https://zoom.us/j/97732215148?pwd=Z0FBNXNFSy9mRUx3UVk4alE4MlRHdz09 Meeting ID: 977 3221 5148 Passcode: 801074 One tap mobile +19292056099,,97732215148#,,,,*801074# US (New York) +13017158592,,97732215148#,,,,*801074# US (Washington DC) Dial by your location +1 929 205 6099 US (New York) +1 301 715 8592 US (Washington DC) +1 312 626 6799 US (Chicago) +1 669 900 6833 US (San Jose) +1 253 215 8782 US (Tacoma) +1 346 248 7799 US (Houston) Meeting ID: 977 3221 5148 Passcode: 801074 Find your local number: https://zoom.us/u/aecn4pJKSi

TBA

Defining canonically best factorization theorems for the generating functions of special convolution type sums

Series
Algebra Seminar
Time
Wednesday, February 10, 2021 - 15:30 for 1 hour (actually 50 minutes)
Location
ONLINE
Speaker
Maxie Schmidt

We are motivated by invertible matrix based constructions for expressing the coefficients of ordinary generating functions of special convolution type sums. The sum types we consider typically arise in classical number theoretic applications such as in expressing the Dirichlet convolutions $f \ast 1$ for any arithmetic function $f$. The starting point for this perspective is to consider the so-termed Lambert series generating function (LGF) factorization theorems that have been published over the past few years in work by Merca, Mousavi and Schmidt (collectively). In the LGF case, we are able to connect functions and constructions like divisor sums from multiplicative number theory to standard functions in the more additive theory of partitions. A natural question is to ask how we can replicate this type of unique "best possible", or most expressive expansion relating the generating functions of more general classes of convolution sums? In the talk, we start by summarizing the published results and work on this topic, and then move on to exploring how to define the notion of a "canonically best" factorization theorem to characterize this type of sum in more generality.

BlueJeans link: https://bluejeans.com/936847924

The two-weight inequality for Calderon-Zygmund operators with applications and results on two weight commutators of maximal functions on spaces of homogeneous type.

Series
Analysis Seminar
Time
Wednesday, February 10, 2021 - 14:00 for 1 hour (actually 50 minutes)
Location
https://us02web.zoom.us/j/71579248210?pwd=d2VPck1CbjltZStURWRWUUgwTFVLZz09
Speaker
Manasa VempatiWashington University in St Louis

For (X,d,w) be a space of homogeneous type in the sense of Coifman and Weiss, suppose that u and v are two locally finite positive Borel measures on (X,d,w).  Subject to the pair of weights satisfying a side condition, we characterize the boundedness of a Calderon--Zygmund operator T from L^{2}(u) to L^{2}(v) in terms of the A_{2} condition and two testing conditions. The proof uses stopping cubes and corona decompositions originating in work of Nazarov, Treil and Volberg, along with the pivotal side condition.

We also give the two weight quantitative estimates for the commutator of maximal functions and the maximal commutators with respect to the symbol in weighted BMO space on spaces of homogeneous type. These commutators turn out to be controlled by the sparse operators in the setting of space of homogeneous type. The lower bound of the maximal commutator is also obtained.

Zoom link:

https://us02web.zoom.us/j/71579248210?pwd=d2VPck1CbjltZStURWRWUUgwTFVLZz09

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