Spring 2024: Fridays at 2:30pm, Fretwell 302
January 19: Xingjie Li (UNC Charlotte)
- Title: Robust and fast differentiation for Sinkhorn optimal transport
- Abstract: Shuffled linear regression has been exploring under great generality the recovery of signals from subsampled and permuted measurements. In this talk, I will review the state-of-art theories and methods for solving shuffled linear regression, in particular by the optimal transport method. I will then introduce the computation of the derivatives of the loss function, the analytical expression, properties and numerical challenges. Finally, I will display our on-going work on a new method which addresses these numerical challenges. This is a joint work with Dr Fei Lu from Johns Hopkins, Dr Molei Tao from Georgia Tech and Dr Felix Ye from University of Albany.
January 26: Robert Bland (UNC Charlotte)
- Title: Integer maps with dynamics similar to the Collatz map
- Abstract: The infamous Collatz map has very complicated and chaotic dynamics for a general input, but much can be said about the statistical or average behavior of the map for a “typical” choice of input by way of a 2-adic analysis. In this talk, I will discuss a class of maps on $\mathbb{Z}$ with similar structure and dynamics as the Collatz map, the residue class-wise affine (RCWA) maps, which can be analysed with a similar $d$-adic framework. I will also present a result that extends a 1992 theorem by Ivan Korec on the Collatz map to all RCWA maps of “relatively prime” type with mean coefficient $< 1$.
February 2: Kevin McGoff. Important: this talk will begin at 3:00pm, not the usual 2:30pm!
- Title: An introduction to symbolic dynamics on groups
- Abstract: Symbolic dynamical systems serve as model systems in the study of topological dynamics and group actions, and they exhibit a wide variety of interesting behaviors. In this talk I will define some of the core concepts, discuss some of the central questions, and state a small sample of results from the field.
February 9: Will Brian (UNC Charlotte)
- Title: Does P(ω)/fin know its right hand from its left? (part 2)
- Abstract: I’m going to talk about an old question of van Douwen: Are the shift map and its inverse conjugate in the automorphism group of P(ω)/fin? By the late 1980’s, van Douwen and Shelah proved that it is consistent they are not conjugate. Specifically, any automorphism witnessing their conjugacy would need to be nontrivial (van Douwen), but it is consistent that all automorphisms are trivial (Shelah). In this talk I’m going to discuss the recently-proved complementary result: it is consistent that the shift map and its inverse are conjugate and, in fact, it follows from CH. This shows that Van Douwen’s question is independent of the usual axioms of set theory, ZFC. While part 1 of this talk was focused on explaining Van Douwen’s problem and what the independence of it means, this talk is focused on highlighting some of the main features of the proof. I will not assume you know anything about axiomatic set theory, and I will not assume that you remember anything from part 1 of this talk.
February 16: Kevin McGoff
- Title: Symbolic dynamics on groups (Part II)
- Abstract: Symbolic dynamical systems serve as model systems in the study of topological dynamics and group actions, and they exhibit a wide variety of interesting behaviors. In this talk I will define some of the core concepts, discuss some of the central questions, and state a small sample of results from the field. This talk will be a continuation of my previous talk (February 2), but I hope to make it understandable even if you didn’t attend Part I.
February 23: Kitty Yang (UNC Asheville)
- Title: Language stable subshifts and characteristic measures
- Abstract: Cyr and Kra recently defined a class of subshifts called language stable subshifts, which are shifts that are particularly well-approximated by shifts of finite type. They showed that language stable subshifts carry a characteristic measure, which is a probability measure which is invariant under the action of the automorphism group. We will discuss the proof, some examples, and possible extensions to more general G-subshifts.
March 1: no talk
March 8: Spring Topology and Dynamics Conference (https://pages.charlotte.edu/stdc2024/)
March 15: no talk
March 22: Phuong Hoang (UNC Charlotte)
- Title: Detecting graph isomorphisms between weighted undirected graphs via optimal transport
- Abstract: In the previous talk, we introduced a new kind of optimal transport problem called optimal reversible transition couplings (ORTC). Today, we will talk about our recent work in which we apply the ORTC to detect isomorphisms between two undirected graphs. More specifically, we provide some conditions on the graphs and on the cost function such that the following relation holds: the ORTC cost between two graphs equals zero if and only if there is an isomorphism between them. Unlike previous methods, the technique we use derives from stochastic processes and symbolic dynamics.
March 29: no talk
April 5: no talk
April 12: Carolina Dynamics Symposium: Van Cyr
April 19:
April 26:
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Fall 2023 meeting details: Fridays at 2pm, Fretwell 302
September 1: Robert Bland, An embedding theorem for subshifts over amenable groups with the comparison property, arxiv link to paper: https://arxiv.org/abs/2211.00215
September 8: No meeting
September 15: Jey Raymond, Shifts of Finite Type on Locally Finite Groups, arxiv link to paper: https://arxiv.org/abs/2304.07582
September 22: Sergei Miles, Dynamics of the shift action on linear sequence spaces over groups beyond Z
September 29:
October 6: Harrison Latimer
October 13: Will Brian
October 20: Hal West
October 27: Shengwen Guo
November 3: Phuong Hoang
November 10: No meeting
November 17: Xingjie Li
November 24: No meeting
December 1: