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

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) 

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) 

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

Preprint Algebra Seminar  Strong and weak Fregularity are equivalent for graded rings, by Smith and Lyubeznik Speaker: Rankeya Datta 

Algebra Seminar  The log minimal model program for excellent threefolds The log minimal model program has recently been completed for klt threefolds over excellent base schemes of residue characteristic p>5�>5. In this talk I will survey the known results, together with some motivations and applications for working in this more general setup. The passcode is: 967345 Speaker: Joe Waldron (Michigan State University) 

Algebra Seminar  Deformation of canonical maps and its applications to moduli space of varieties of general type A framework was developed in a joint work with F. J. Gallego and M. Gonzalez to systematically deal with the deformation of finite morphisms, multiple scheme structures on algebraic varieties and their smoothing. There are several applications of this framework. In this talk I will talk about some of them. First is the description of some components of the moduli space of varieties of general type in all dimensions. In particular, we show the existence of components of the moduli space of general type in all dimensions that are analogue of the moduli space of curves of genus g≥2�≥2. Secondly, we give a new method to construct smooth varieties in projective space embedded by complete sub canonical linear series within the range of the Hartshorne conjecture and beyond. Are all of them complete intersections? We also construct systematically, smooth non complete intersection subvarieties embedded by complete linear series outside the range of the Hartshorne conjecture. As a byproduct, we construct simple canonical varieties of any dimension, expanding the original question posed by Enriques for algebraic surfaces. This is joint work with F. J. Gallego, J. Mukherjee and D. Raychaudhury. Speaker: Purnaprajna Bangere (University of Kansas) 

Preprint Algebra Seminar  Introduction to characteristic p methods continued Speaker: Ian Aberbach 