Schedule and Abstracts

All talks took place in Avery Hall 106. Refreshments were found in Avery Hall 110.
Avery Hall Floorplan

The tentative schedule is:
 Saturday, April 28, 2018 10:30 – 10:50 Registration 10:50 – 11:00 Opening Remarks 11:00 – 11:20 TBA TBA *11:30 – 12:10 TBA TBA 12:10 – 2:00 Lunch 2:00 – 2:20 TBA TBA *2:30 – 3:10 TBA TBA 3:20 – 3:40 TBA TBA 3:40 – 4:00 20 minute break *4:00 – 4:40 TBA TBA 4:50 – 5:10 TBA
 Sunday, April 29, 2018 8:45 – 9:20 Coffee and Snacks *9:30 – 10:10 TBA TBA 10:20 – 10:40 TBA TBA *10:50 – 11:30 TBA TBA 11:40 – 12:00 TBA TBA 12:10 Closing Remarks
*40 Minute Talk

• Liliam Carsava Merighe; TBA
Abstract: Let $(R,\mathfrak{m})$ be a commutative Noetherian complete local ring. Motivated by a Rees' question, in this work we study which is the relationship between $\overline{\mathfrak{b}}$, the classical Northcott-Rees integral closure of $\mathfrak{b}$, and $\mathfrak{b}^{*(H)}$, the integral closure of $\mathfrak{b}$ relative to an Artinian $R$-module $H$. We conclude they are equal when every minimal prime ideal of $R$ belongs to $\mathrm{Att}_R(H)$. As application, we show what happens when $H$ is a generalized local cohomology module.

• Eloísa Grifo; Homological algebra vs symbolic powers
Abstract: The containment problem for symbolic and ordinary powers of ideals asks when the containment $I^{(a)} \subseteq I^b$ holds. Under nice enough conditions, we can replace this question by a purely homological one: whether or not a certain map between Ext modules vanishes. We will answer this question for certain classes of ideals $I$, and long the way compute free resolutions for all $I^n$ using Rees Algebra techniques.

• Michael Perlman; Regularity of Pfaffian thickenings
Abstract: Let $S$ be the ring of polynomial functions on the space of $n \times n$ complex skew-symmetric matrices. This ring has a natural action of the group $GL(n)$. For every invariant ideal $I$ in $S$, we compute the modules $\text{Ext}^i(S/I,S)$, and as a consequence we obtain formulas for the Castelnuovo-Mumford regularity of powers and symbolic powers of ideals of Pfaffians. This allows us to characterize when powers of ideals of Pfaffians have linear minimal free resolution.