Date 
Speaker 
Title/Abstract 
9/7 
Lance Miller (UArk) 
The de RhamWitt complex and the htopology
In this series of talks, we will discuss differential forms on singular schemes. Usually, one must impose some condition to make discussions fruitful, for example to consider normal schemes. We will first survey work of Huber and Joerder, and following work of Huber, Kebekus, and Kelly on how to unify many different perspectives on differential forms using Voevodsky's htopology. We then apply these ideas to Illusie's de RhamWitt complex which is joint work with V. Ertl.

9/14 
Lance Miller (UArk) 
The de RhamWitt complex and the htopology
Continuation of last week's talk.

9/21 
Paolo Mantero (UArk) 
Properties of Reeslike algebras
Reeslike algebras have been used by McCullough and Peeva to construct counterexamples to the more general statement of the EisenbudGoto regularity conjecture. In this talk, we will explore some of their algebraic and geometric properties and illustrate some structural results. This talk is based on joint work with J. McCullough and L. E. Miller.

10/5 4:10pm 
Youngsu Kim (UArk) 
Generic links of determinantal varieties.
We study singularities of the generic link of a determinantal variety. Let A denote an affine space over the complex numbers, and let X and Y be reduced equidimensional subschemes of A. We say that X and Y are linked via V if there exists a complete intersection V in A such that I_X = I_V : I_Y and I_Y= I_V : I_X.
Two linked subschemes have many properties in common, and it is believed that the generic link of a variety improves singularities of the variety. Let X be a variety and Y the generic link of X. Wenbo Niu showed that the log canonical threshold, lct for short, “improves” under taking the generic link, i.e., lct Y is greater than lct X. It is not known if equality holds in general. In this talk, we show that in the case where X is a determinantal variety, we have lct X = lct Y. This is joint work with Wenbo Niu and Lance Edward Miller.

10/10 4:10pm 
Alex Buium (UNM) 
Lie invariance of Frobenius lifts
We show that the padic completion of any affine elliptic curve with ordinary reduction
possesses Frobenius lifts whose "normalized" action on 1forms preserves mod p the space of invariant 1forms. We also show that, after removing the 2torsion sections,
the above situation can be "infinitesimally deformed" in the sense that
the above mod p result has a mod p^2 analogue. Finally we show that the mod p result
fails for linear algebraic groups that are not tori.

10/19 
William Taylor (TSU) 
TBA
TBA

10/26 
Jesse Keyton (UArk) 
TBA
TBA

11/2 4:10pm 
Alessandra Costantini (Purdue) 
CohenMacaulayness of Rees algebras of modules
Rees algebras of ideals and modules arise in Algebraic Geometry as homogeneous coordinate rings of blow up or as graphs of rational maps. The CohenMacaulayness of the Rees algebra of an ideal I is wellunderstood in connection with the CohenMacaulayness of the associated graded ring of I, thanks to results of Huneke, Trung and Ikeda. However, there is no module analogue for the associated graded ring, so the study of CohenMacaulayness of Rees algebras of modules requires completely different techniques. In this talk, we will provide a sufficient condition for the Rees algebra of a module to be CohenMacaulay. Our result generalize results of Johnson and Ulrich, and of Goto, Nakamura and Nishida.

11/6 
Sean SatherWagstaff (Clemson) 
TBA
TBA

11/9 
Youngsu Kim (UArk) 
Generic links of determinantal varieties Part II.
We study singularities of the generic link of a determinantal variety. Let A denote an affine space over the complex numbers, and let X and Y be reduced equidimensional subschemes of A. We say that X and Y are linked via V if there exists a complete intersection V in A such that I_X = I_V : I_Y and I_Y= I_V : I_X.
Two linked subschemes have many properties in common, and it is believed that the generic link of a variety improves singularities of the variety. Let X be a variety and Y the generic link of X. Wenbo Niu showed that the log canonical threshold, lct for short, “improves” under taking the generic link, i.e., lct Y is greater than lct X. It is not known if equality holds in general. In this talk, we show that in the case where X is a determinantal variety, we have lct X = lct Y. This is joint work with Wenbo Niu and Lance Edward Miller.
