The Mathematics Department holds regular seminars on a variety of topics. Please see below for further details.
Seminars
Seminar  Meeting Details  Title & Abstract 

Differential Equations Seminar  Desingularization of hollow vortices A hollow vortex is a region of constant pressure bounded by a vortex sheet and suspended inside a perfect fluid — think of it as a spinning bubble of air in water. In this talk, I will describe a general method for desingularizing nondegenerate translating, rotating, or stationary point vortex configurations into collections of steady hollow vortices. Through global bifurcation theory, moreover, these families can be extended to maximal curves of solutions that continue until the onset of a singularity. As specific applications, this machinery gives the first existence theory for corotating hollow vortex pairs and stationary hollow vortex tripoles, as well as a new construction of Pocklington’s classical cotranslating hollow vortex pairs. All of these families extend into the nonperturbative regime, and we obtain a rather complete characterization of the limiting behavior along the global bifurcation curve. This is joint work with Ming Chen (University of Pittsburgh) and Miles H. Wheeler (University of Bath). Speaker: Samuel Walsh (University of Missouri) 

Differential Equations Seminar  New results on global bifurcation of traveling periodic water waves While the research on water waves modeled by Euler's equations has a long history, mainly in the last two decades traveling periodic rotational waves have been constructed rigorously by means of bifurcation theorems. After introducing the problem, I will present a new reformulation in two dimensions in the puregravity case, where the problem is equivalently cast into the form “identity plus compact”, which is amenable to Rabinowitz's global bifurcation theorem. The main advantages (and the novelty) of this new reformulation are that no simplifying restrictions on the geometry of the surface profile and no simplifying assumptions on the vorticity distribution (and thus no assumptions regarding the absence of stagnation points or critical layers) have to be made. Within the scope of this new formulation, global families of solutions, bifurcating from laminar flows with a flat surface, are constructed. Moreover, I will discuss the possible alternatives for the global set of solutions, as well as their nodal properties. This is joint work with Erik Wahlén. Speaker: Jörg Weber (Lund University) 

Astro/Relativity Seminar  Astro/Relativity Seminars Please see the schedule here. 

Preprint Algebra Seminar  Asymptotic multiplicities of graded families of ideals and linear series, Part II Speaker: Stephen Landsittel 

Differential Equations Seminar  Antiplane shear equilibria in the large In this talk, we discuss antiplane shear deformations on a semiinfinite slab with a nonlinear mixed traction displacement boundary condition. We apply global bifurcation theoretic methods and deduce extreme behavior at the terminal end solution curves. It is shown that arbitrarily large strains are encountered for a class of idealized materials. We also consider degenerate materials, prove that ellipticity breaks down, and show that a concurrent blowup in the second derivative occurs. Speaker: Thomas Hogancamp (University of Missouri) 

Preprint Algebra Seminar  Asymptotic multiplicities of graded families of ideals and linear series, by Cutkosky (Part I) Speaker: Stephen Landsittel 

Algebra Seminar  Analytic spread and symbolic analytic spread The analytic spread of a module M is the minimal number of generators of a submodule that has the same integral closure as M. In this talk, we will present a result that expresses the analytic spread of a decomposable module in terms of the analytic spread of its component ideals. In the second part of the talk, we will show an upper bound for the symbolic analytic spread of ideals of small dimension. The latter notion is the analogue of analytic spread for symbolic powers. These results are joint work with Carles BiviàAusina and Hailong Dao, respectively. Speaker: Jonathan Montaño (New Mexico State University) 

Differential Equations Seminar  Padé approximants to time series: Some techniques and applications The Gtransform to a data series is the extension of the Fourier transform from the unit circle to the entire complex plane.I shall introduce the Padé approximant to the Gtransform and discuss some of its properties as regard its poles, zeros, and the residues. In particular, I’ll show examples of superresolution with respect to the Nyquist limit, numerical evidence of universality for the behavior of poles and zeros associated with noise and how the presence of signals alters that behavior. I’ll conclude showing a couple of applications. In particular, work in progress on brain waves. Speaker: Luca Perotti (Texas Southern University) 

Preprint Algebra Seminar  Strong and weak Fregularity are equivalent for graded rings, Part III Speaker: Rankeya Datta 

Algebra Seminar  Generic local duality and purity exponents Let \(R\) be a Noetherian ring, \(P\) be a prime ideal of \(R\) such that \(R_P\) is CohenMacaulay of dimension \(h\), \(\omega\) be a finitely generated \(R\)module such that \(\omega_P\) is a canonical module for \(R_P\), and \(W\) be a subset of \(R\) that naturally maps onto the set of nonzero elements of \(R/P\). We show that for every finitely generated $R$module $M$, there exists \(g \in W\) such that \(H_P^j(M)_g \cong Hom(Ext_R^{hj}(M, \omega), H_P^h(\omega))_g\), which gives the wellknown local duality when we localize at \(P\). Moreover, each \(H_P^j(M)_g\) has an ascending filtration such that all the factors are free over \(R/P\). We use this result to study the purity exponents in Noetherian rings of prime characteristic \(p\). In the case where \(R\) is excellent CohenMacaulay (this assumption can be weakened), we establish an upper semicontinuity result for the purity exponent considered as a function on the spectrum of \(R\). This result enables us to prove that excellent strongly Fregular rings are very strongly Fregular (also called Fpure regular). Another consequence is that the Fpure locus is open in an excellent CohenMacaulay ring. This is joint work with Mel Hochster. Speaker: Yongwei Yao (Georgia State University) 