| Monday, February 13, 2023 | ||
|---|---|---|
| 3:00-4:15 PM | 4088 East Hall | RTG Number Theory Seminar -- Patrick Daniels (UM) |
| 4:00-5:00 PM | EH 3866 East Hall | Student Combinatorics:The Picard Group of a Graph -- Benjamin Baily |
| 4:30-5:30 PM | 4088 East Hall | Group, Lie and Number Theory Seminar -- Cheng-Chiang Tsai |
| Tuesday, February 14, 2023 | ||
| 3:00-4:00 PM | 3866 East Hall | Student CA Seminar: Commutative Algebra Social -- |
| 4:00-5:00 PM | 1360 East Hall | Colloquium: Galois groups in Enumerative Geometry and Applications -- Frank Sottile (Texas A & M University) |
| Wednesday, February 15, 2023 | ||
| 2:30-4:00 PM | 4088 East Hall | Criteria for smoothness of Schubert varieties -- Terrence George |
| 3:00-4:00 PM | 1866 East Hall | Student Arithmetic: Hida Families -- Alex Bauman |
| 4:00-5:00 PM | 1360 East Hall | Projections in positively curved spaces with applications to causal inference and economics -- Florian Gunsilius |
| 4:00-5:30 PM | 4096 East Hall | Algebraic Geometry seminar: Topological aspects in algebraic optimization -- Botong Wang (University of Wisconsin) |
| 4:00-5:30 PM | Logic Seminar: The omega-Vaught's Conjecture -- David Gonzalez | |
| 4:00-5:20 PM | 3866 East Hall | RTG Seminar on Geometry, Topology and Dynamics - - Geometry and analysis on buildings -- Carsten Peterson (U Michigan) |
| Thursday, February 16, 2023 | ||
| 4:00-5:20 PM | 4096 East Hall | K-stability learning seminar: Filtrations revisited and uniform K-stability -- Bradley Dirks |
| 4:00-5:00 PM | 1866 East Hall | Student DGT: Microlocal analysis in dynamics -- Katia Shchetka |
| Friday, February 17, 2023 | ||
| 3:00-4:00 PM | 1084 East Hall | AIM Seminar: Wave patterns generated by large-amplitude rogue waves and their universal character -- Deniz Bilman, University of Cincinnati |
| 3:00-4:00 PM | 4088 East Hall | Combinatorics Seminar: The equivariant Hilbert series and formal languages -- Aida Maraj (University of Michigan) |
| 3:00-3:50 PM | 2866 East Hall | Student Algebraic Geometry: K3 Surfaces -- Saket Shah |
| 4:00-5:30 PM | 4096 East Hall | Preprint Algebraic Geometry Seminar: Numerical dimension of algebraic fiber spaces in positive characteristic, after Ejiri -- Swaraj Pande |
| 4:00-5:00 PM | 2866 East Hall | Student AIM Seminar: Numerical Methods for Vorticity Dynamics on a Sphere -- Anthony Chen, University of Michigan |
| 4:00-5:00 PM | 4088 East Hall | GLNT: p-adic Measures for Reciprocals of L-functions -- Razan Taha (Rose Hulman) |
| 4:00-4:50 PM | 3866 East Hall | GEOMETRY SEMINAR. - On dimension theory of random walks and group actions by circle diffeomorphisms -- DISHENG XU (Great Bay University) |
Date/Time: Monday, February 13, 2023, 3:00-4:15 PM
Speaker: Patrick Daniels (UM)
Location: 4088 East Hall
Abstract: Title: Integral models of Shimura varieties
Date/Time: Monday, February 13, 2023, 4:00-5:00 PM
Speaker: Benjamin Baily
Location: EH 3866 East Hall
Abstract: A divisor on a graph is an assignment of integer weights to each of the vertices. One assignment is considered linearly equivalent to another assignment if it can be transformed into it by a series of legal moves called chip-firing moves. The Picard group of a graph, named based on its relationship to the Picard group of a scheme, is defined as the free abelian group of divisors on the graph up to linear equivalence. This group will be the central focus of the talk, and we'll compute Pic(G) for some classes of graphs G. We'll also define the rank of a divisor and a related graph invariant called gonality.
Date/Time: Monday, February 13, 2023, 4:30-5:30 PM
Speaker: Cheng-Chiang Tsai
Location: 4088 East Hall
Abstract: Title: Wave-front sets and graded Springer theory
Abstract: For a character of a p-adic reductive group there is the notion of wave-front set, which is a set of nilpotent orbits that describes the asymptotic behavior of the character near the identity. By a theorem of Moeglin-Waldspurger, it also describes the least degenerate Whittaker models, which is a double generalization of local components of Fourier expansions for modular forms.
There is the conjecture that any wave-front set is contained in a single geometric orbit. This conjecture is confirmed for many cases of depth-0 representations, based on Lusztig's work on the analogous wave-front set question over the residue field. In this talk, we explain how the above conjecture does not hold in general, in particular not for a depth-1/2 representation we will construct, because the analogous conjecture does not hold for graded Lie algebras. This last observation is inspired by Springer theory for graded Lie algebras, which we hope to briefly talk about.
Date/Time: Tuesday, February 14, 2023, 3:00-4:00 PM
Speaker:
Location: 3866 East Hall
Abstract: Event is now hybrid!
Come join us for snacks and socializing! This event is an opportunity to get to know the other people in the department who are interested in commutative algebra or other related fields.
This event is open to
undergraduates, grad students, and postdocs. Please let us know by Monday afternoon if you have any dietary restrictions. Zoom link provided via studentcommalg listserv, email annabro or swarajsp if you are not on the listserv (or missed the email) and would would like the zoom meeting info.
Date/Time: Tuesday, February 14, 2023, 4:00-5:00 PM
Speaker: Frank Sottile (Texas A & M University)
Location: 1360 East Hall
Abstract: In 1870 Jordan explained how Galois theory can be applied
to problems from enumerative geometry, with the group encoding
intrinsic structure of the problem. Earlier Hermite showed
the equivalence of Galois groups with geometric monodromy
groups, and in 1979 Harris initiated the modern study of
Galois groups of enumerative problems. He posited that
a Galois group should be `as large as possible' in that it
will be the largest group preserving internal symmetry in
the geometric problem.
I will describe this background and discuss some work
in a long-term project to compute, study, and use Galois
groups of geometric problems, including those that arise
in applications of algebraic geometry. A main focus is
to understand Galois groups in the Schubert calculus, a
well-understood class of geometric problems that has long
served as a laboratory for testing new ideas in enumerative geometry.
Date/Time: Wednesday, February 15, 2023, 2:30-4:00 PM
Speaker: Terrence George
Location: 4088 East Hall
Abstract: We will discuss several combinatorial characterizations of smooth Schubert varieties due to Lakshmibai and Sandhya, and Carrell and Petersen.
Date/Time: Wednesday, February 15, 2023, 3:00-4:00 PM
Speaker: Alex Bauman
Location: 1866 East Hall
Abstract: We will discuss Hida's construction of ordinary families of modular forms, which interpolate the Fourier coefficients of classical modular forms p-adically. We will give applications of this theory to special values of L-functions and Galois representations. The only prerequisites are basics about modular forms and p-adic numbers.
Date/Time: Wednesday, February 15, 2023, 4:00-5:00 PM
Speaker: Florian Gunsilius
Location: 1360 East Hall
Abstract: I present an overview of recent research on defining projections in general positively-curved spaces (PC spaces), in particular the 2-Wasserstein space and the Gromov-Wasserstein space defined on metric measure spaces. I will highlight applications to economics and causal inference. This talk is based on joint works with Meng Hsuan Hsieh, Myung Jin Lee, and Yiman Ren.
Date/Time: Wednesday, February 15, 2023, 4:00-5:30 PM
Speaker: Botong Wang (University of Wisconsin)
Location: 4096 East Hall
Abstract: We will survey some recent works relating the algebraic degree of optimization problems and the topological Euler characteristics. More specifically, the topological formulas for Maximum Likelihood degree and Euclidean Distance degree will be discussed. We will also explore deeper relations between the algebraic bidegrees in optimization problems and Chern classes. The results are joint works with Laurentiu Maxim, Jose Rodriguez and Lei Wu.
Date/Time: Wednesday, February 15, 2023, 4:00-5:30 PM
Speaker: David Gonzalez
Location:
Abstract: Robert Vaught conjectured that the number of countable models of any given list of axioms must be either countable or continuum, but never in between. Despite all the work that has gone into this conjecture over the past sixty years, it remains open. It is one of the most well-known, long-standing open questions in mathematical logic. We introduce the omega-Vaught's conjecture, a strengthening of Vaught's conjecture for infinitary logic. We believe that a structural proof of Vaught's conjecture for infinitary logic would actually be a proof of the omega-Vaught's conjecture. Furthermore, a counterexample to the omega-Vaught's conjecture would likely contain ideas helpful in constructing a counterexample to Vaught's conjecture.
We prove the omega-Vaught's conjecture for linear orderings, a strengthening of Vaught's conjecture for linear orderings originally proved by Steel. The proof notably differs from Steel's proof (and any other previously known proof of Vaught's conjecture for linear orderings) in that it makes no appeal to lemmas from higher computability theory or descriptive set theory.
In this talk I will assume minimal background knowledge on Vaught's conjecture and spend some time going over the needed foundational information. Through this discussion, we will naturally arrive at the definition of the omega-Vaught's conjecture and I will explain some of the main tools used in the linear order proof. I will focus on highlighting a concrete, plausible, potential path to a proof of Vaught's conjecture.
This talk is based on joint work with Antonio Montalban.
Date/Time: Wednesday, February 15, 2023, 4:00-5:20 PM
Speaker: Carsten Peterson (U Michigan)
Location: 3866 East Hall
Abstract: Buildings are simplicial complexes which serve as combinatorial analogues of many important geometric spaces such as flag manifolds and symmetric spaces. In this talk we shall focus on illustrating many ideas related to buildings via the case of the Bruhat-Tits building associated to $SL(n, F)$, where $F$ is a non-archimedean local field. Such buildings may be viewed as non-archimedean analogues of the (perhaps) more familiar symmetric spaces $SL(n, R)/SO(n)$ (such as the hyperbolic plane). We shall discuss how the group theory of $SL(n, F)$ relates to the geometry of the building, and how the representation theory of $SL(n, F)$ relates to the analysis of functions on the building. Time permitting, we shall also discuss how these ideas show up in recent work of mine regarding "quantum ergodicity for $SL(3, F)$".
Date/Time: Thursday, February 16, 2023, 4:00-5:20 PM
Speaker: Bradley Dirks
Location: 4096 East Hall
Abstract: S (volume) and T-invariants of a filtration; Define uniform K-stability.
Date/Time: Thursday, February 16, 2023, 4:00-5:00 PM
Speaker: Katia Shchetka
Location: 1866 East Hall
Abstract: In these two lecture series, we'll delve into the world of microlocal analysis and its applications in dynamics. In the first lecture, I'll introduce you to pseudo-differential calculus. We will axiomatize these objects and establish the key properties they enjoy. Pseudo-differential operators are used to make sense of a "function of differential operators." This is achieved through a simple trick: using the Fourier transform, differential operators become merely polynomials. With a bit more care, you can define many other types of "functions of differential operators." No prior knowledge is required. Welcome!
Date/Time: Friday, February 17, 2023, 3:00-4:00 PM
Speaker: Deniz Bilman, University of Cincinnati
Location: 1084 East Hall
Abstract: It is known from our recent work that both fundamental rogue wave solutions (with Peter Miller and Liming Ling) and multi-pole soliton solutions (with Robert Buckingham) of the nonlinear Schrödinger (NLS) equation exhibit the same universal asymptotic behavior in the limit of large order in a shrinking region near their peak amplitude point, despite the quite different boundary conditions these solutions satisfy at infinity. This behavior is described by a special solution of again the NLS equation that also satisfies ordinary differential equations from the Painlevé-III hierarchy. We review these results and show that this profile also arises universally from arbitrary background fields. We then show how rogue waves and solitons of arbitrary orders can be placed within a common analytical framework in which the "order" becomes a continuous parameter, allowing one to tune continuously between types of solutions satisfying different boundary conditions. In this framework, solitons and rogue waves of increasing integer orders alternate as the continuous order parameter increases. We show that in a bounded region of the space-time of size proportional to the order, these solutions all appear to be the same when the order is large. However, in the unbounded complementary region one sees qualitatively different asymptotic behavior along different sequences. This is joint work with Peter Miller (U. Michigan).
Date/Time: Friday, February 17, 2023, 3:00-4:00 PM
Speaker: Aida Maraj (University of Michigan)
Location: 4088 East Hall
Abstract: Motivated by statistical models with varying numbers of parameters, in the past decade there has been an interest in asymptotic phenomena for infinitely many objects such as ideals and algebras related by a group action. We can record detailed quantitative data for infinitely many related objects in a multivariate formal power series, which we call the equivariant Hilbert series. The rational form of these series, if it exists, is of interest as it can provide additional data about the objects in study. In searching for this rational form, we utilize theory of languages and their automata from computer science. For a language and a weight function on it, the sum of weights of words in the language is a multivariate formal power series. This series has a always rational presentation when the language satisfies certain rules determined by a directed graph on a finite number of nodes, commonly known as a regular language. The rational form can be easily computed via the graph. Now, given a family of related algebraic objects, we search for regular languages and weights on them such that their formal power series equals the equivariant Hilbert series for our related objects. The talk will be introductory and is based on is based on
https://arxiv.org/abs/2204.07849 and
https://arxiv.org/abs/1909.13026. No knowledge on Hilbert series or languages will be assumed.
Date/Time: Friday, February 17, 2023, 3:00-3:50 PM
Speaker: Saket Shah
Location: 2866 East Hall
Abstract: K3 surfaces are surfaces with trivial canonical bundle and vanishing first cohomology of the structure sheaf; they are one of the most well-studied classes of Calabi-Yau varieties. I will present some of their basic properties and discuss how they are in essence completely determined by their Hodge theory via the Global Torelli theorem. Time permitting, I will make some remarks about a derived generalization of the Torelli theorem.
Date/Time: Friday, February 17, 2023, 4:00-5:30 PM
Speaker: Swaraj Pande
Location: 4096 East Hall
Abstract: N/A
Date/Time: Friday, February 17, 2023, 4:00-5:00 PM
Speaker: Anthony Chen, University of Michigan
Location: 2866 East Hall
Abstract: The Barotropic Vorticity Equation describes the balance of vorticity and the Coriolis force for a fluid moving on a rotating sphere, and is important in geophysical fluid dynamics. In this talk, I will discuss some numerical considerations, first presenting some basics of geophysical fluid dynamics, before presenting a short derivation of the barotropic vorticity equation, and then moving on to discuss various numerical aspects of the problem. I will focus on a Lagrangian particle discretization, as well as a new fast summation technique based on a spherical tree code. I will also touch on the role of adaptive mesh refinement.
Date/Time: Friday, February 17, 2023, 4:00-5:00 PM
Speaker: Razan Taha (Rose Hulman)
Location: 4088 East Hall
Abstract: Abstract: In 2014, Gelbart, Miller, Panchishkin, and Shahidi introduced a p-adic analog to part of the Langlands-Shahidi method by studying the reciprocal of the p-adic L-function through the Fourier series expansion of Eisenstein series on SL_2(Z). In this talk, I discuss an analogous result in the case where K is a totally real number field. More precisely, I will construct a certain p-adic measure whose Mellin transform is the reciprocal of the Deligne-Ribet p-adic L-function. This construction arises from the analysis of the non-constant Fourier coefficients of the Eisenstein series on the Hilbert modular group SL_2(O_K).
Date/Time: Friday, February 17, 2023, 4:00-4:50 PM
Speaker: DISHENG XU (Great Bay University)
Location: 3866 East Hall
Abstract: In this talk I will present a joint work with W. He and Y. Jiao. We study the random walks and group actions by circle diffeomorphisms. Under mild assumptions we establish several results on the dimensional properties of invariant measures and attractors (limit sets or minimal sets). Our results include exact dimensionality and dimension formula of stationary measures, variational principles for dimensions in various settings, estimates of Hausdorff dimension of exceptional minimal set, etc. We also show an approximation theorem for random walks by circle diffeomorphisms which is analogous to the results of Katok, Avila-Crovisier-Wilkinson, Morris-Shmerkin.