Events for 09/14/2016 from all calendars

Number Theory Seminar

Time: 1:45PM - 2:45PM

Location: BLOC 220

Speaker: Nathan Green, Texas A&M University

Title: Formulas for Special Values of L-functions in Drinfeld Modules

Abstract: We study the arithmetic of coordinate rings of elliptic curves in finite characteristic and analyze their connection with Drinfeld modules. Using the functional equation for the shtuka function, we find identities for power sums and twisted power sums over these coordinate rings which allow us to express function field zeta values in terms of Drinfeld logarithms and recover a log-algebraicity result of Anderson. Moreover, our results allow for the explicit computation of these power sums. Joint with M. Papanikolas.

URL: Event link

Noncommutative Geometry Seminar

Time: 2:00PM - 2:50PM

Location: BLOC 628

Speaker: Kun Wang, Texas A&M University

Title: The Cuntz Semi-group and the Elliott invariant

Abstract: In my talk, I will introduce the Cuntz semi-group and the Elliott invariant. I will show some relation between them. In particular, the Cuntz semi-group can be recovered from the Elliott invariant in some cases.

Groups and Dynamics Seminar

Time: 3:00PM - 4:00PM

Location: BLOC 220

Speaker: Zoran Sunic, Texas A&M University

Title: Hanoi Towers Group II

Abstract: This will be the second in a series of talks devoted to the Hanoi Towers group H which models the famous XIX century game invented by the French mathematician Lucas (yes, the one from the Lucas sequence).
The group H is a finitely generated, self-similar group acting on a rooted ternary tree in such a way that the Schreier graph of the action on level N models the game played with N disks (the vertices represent the possible configurations and the group generators the possible moves). It can also be viewed as a finitely generated group of isometries of the Cantor set.
The group H has many interesting properties in its own right:
- It is the first first known example of a finitely generated branch group that maps onto the infinite dihedral group.
- It is amenable but not elementary amenable group.
- It is the iterated monodromy group of a post-critically finite rational map on the Riemann sphere.
- Its closure is finitely constrained (in the sense of symbolic dynamics on trees).
- Its Hausdorff dimension is irrational and its limit space is the well known Sierpiński gasket.
- It was the first example of a finitely generated branch group with nontrivial rigid kernel.
- Calculations involving finite dimensional permutational representations of H based on the self-similarity of the group lead to calculation of the spectra of the Sierpiński graphs.
- It has exponential growth.
- It contains a copy of every finite 3-group.
- The elements of the group may be described as finite automata.
- ...
Notable subgroups (Apollonian group, intertwined odometers groups), the higher Hanoi Towers groups (related to versions of the game with more than 3 pegs), and other variations will also be discussed.

Inverse Problems and Machine Learning

Time: 4:00PM - 5:00PM

Location: BLOC 628

Speaker: Zhidong Zhang, Texas A&M University

Title: Fractional diffusion: recovering the distributed fractional derivative from overposed data

Abstract: There has been considerable recent study in “subdiffusion” models that replace the standard parabolic equation model by a one with a fractional derivative in the time variable. There are many ways to look at this newer approach and one such is to realize that the order of the fractional derivative is related to the time scales of the underlying diffusion process. This raises the question of what order α of derivative should be taken and if a single value actually suffices. This has led to models that combine a finite number of these derivatives each with a different fractional exponent α k and different weighting value c k to better model a greater possible range of time scales. Ultimately, one wants to look at a situation that combines derivatives in a continuous way – the so-called distributional model with parameter μ(α). However all of this begs the question of how one determines this “order” of differentiation. Recovering a single fractional value has been an active part of the process from the beginning of fractional diffusion modeling and if this is the only unknown then the markers left by the fractional order derivative are relatively straightforward to determine. In the case of a finite combination of derivatives this becomes much more complex due to the more limited analytic tools available for such equations, but recent progress in this direction has been made,[9, 8]. This paper considers the full distributional model where the order is viewed as a function μ(α) on the interval (0, 1]. We show existence, uniqueness and regularity for an initial-boundary value problem including an important representation theorem in the case of a single spatial variable. This is then used in the inverse problem of recovering the distributional coefficient μ(α) from a time trace of the solution and a uniqueness result is proven.

First Year Graduate Student Seminar

Time: 5:30PM - 6:30PM

Location: BLOC 628

Speaker: Ola Sobieska, Alex Ruys de Perez, and Peter Howard

Title: Outreach opportunities, and other things students should start doing now to prepare for the job search.

AMUSE

Time: 6:00PM - 7:00PM

Location: BLOC 220

Speaker: Dr. Alan Dabney, Texas A&M University, Department of Statistics

Title: Thinking Probabilistically and Statistically

Abstract: We are exposed today to an unprecedented amount of information from a wide variety of sources and of a wide variety of quality. Some claims, such as those made by marketers, may be blatantly biased and misleading. Others are supported by 'published studies' but are nevertheless preliminary and unlikely to be replicated. Others still are supported by carefully-designed studies and experiments that have been replicated and that have consensus support in the scientific community. How should one interact with information today, and how does one know whether or not to believe a particular claim? In this talk, we will explore the principles of both producing and learning from data. Statistical learning principles will be demonstrated using basic probability theory and simulation-based statistical inference in the R statistical software program. Bio: Alan Dabney received a Ph.D. in Biostatistics from the University of Washington and joined the faculty in the Department of Statistics at A&M in 2006. He is currently an Associate Professor and holder of the Eppright Professorship in Undergraduate Teaching Excellence. Dr. Dabney conducts research in biostatistics, bioinformatics, and statistical education. In addition, he serves as Director of Undergraduate Programs in the Department of Statistics, developing and supporting the brand-new B.S. in Statistics. Given the overlap between the undergraduate majors in Math and Statistics, Dr. Dabney and the Department of Statistics invite current Math majors to consider double-majoring in Statistics. For more information on undergraduate Statistics at A&M, see our webpage: https://www.stat.tamu.edu/academics/undergraduate/