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

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 

Algebra Seminar  On convexity of multiplicities of ideal sequences The HilbertSamuel multiplicity of an ideal is a fundamental invariant of singularities of the ideal and is known to satisfy various convexity properties. In this talk, I will discuss more general convexity properties for ideal sequences (rather than single ideals) and provide an application to Chi Li’s normalized volume of a singularity. Speaker: Harold Blum (University of Utah) 

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

Preprint Algebra Seminar  The generators, relations and type of the Backelin Semigroup Speaker: Arun Suresh 

Algebra Seminar  The Strange World of Quotients in Algebraic Geometry In algebraic geometry, the existence and geometry of quotient schemes is a delicate issue. Even when quotients exist, they may not reflect enough properties of the original group action to be useful. The machinery of geometric invariant theory is one prescription for identifying open subsets of the original scheme that admit useful quotients, but it can be shown that there are, in general, other open sets that also admit wellbehaved quotients. In this talk, we examine particular actions of diagonalizable groups on affine space and illustrate the wide variety of properties that quotients arising from this action can have. Speaker: DIllon Lisk (University of Missouri) 