09:15 AM  09:30 AM


Welcome

 Location
 SLMath: Eisenbud Auditorium, Online/Virtual
 Video


 Abstract
 
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09:30 AM  10:30 AM


Modules of Derivations and Applications to Vector Fields
Claudia Polini (University of Notre Dame)

 Location
 SLMath: Eisenbud Auditorium, Online/Virtual
 Video

 Abstract
The talk is concerned with the structure of the module of derivations and its connections with singularities and vector fields of varieties. Modules of derivations are not well understood  despite great advances on the ZariskiLipman conjecture, there is still no complete characterization for when they are free. Our work is partially motivated by a question of Poincaré, who asked how to decide whether a polynomial vector field in the complex plane leaves some algebraic curve invariant. We reformulate this problem in terms of bounding from below the initial degree of the module consisting of all vector fields that leave a fixed curve invariant. This module is a quotient of the module of derivations. We also treat the case of smooth varieties of higher dimension. For plane curves of low genus we establish a correspondence between finer invariants of the module of derivations, such as its graded betti numbers, and properties of the singularities of the curve. This is joint work with Chardin, Hassanzadeh, Simis, and Ulrich.
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10:30 AM  11:00 AM


Break

 Location
 SLMath: Atrium
 Video


 Abstract
 
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11:00 AM  12:00 PM


The Dimension of Cohomological Support Varieties
Eloísa Grifo (University of Nebraska)

 Location
 SLMath: Eisenbud Auditorium, Online/Virtual
 Video

 Abstract
Given a complex of Rmodules M, one can construct a variety that contains homological information about M called the cohomological support variety V_R(M). These have various homological applications – for example, Pollitz showed they can be used to characterize when R is a complete intersection. In this talk, we will discuss the following realizability question: given an appropriately chosen variety V, when can V be realized as V_R(M) for some M? To study this question, we give bounds on the dimension of such varieties. This is joint work with Ben Briggs and Josh Pollitz.
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12:00 PM  02:00 PM


Lunch

 Location
 SLMath: Atrium
 Video


 Abstract
 
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02:00 PM  03:00 PM


Lengths Of Local Cohomology Using Some Surprising Hilbert Kunz Functions
Jennifer Kenkel (Grinnell College)

 Location
 SLMath: Eisenbud Auditorium, Online/Virtual
 Video

 Abstract
We investigate the lengths of certain local cohomology modules over polynomial rings. By fixing the degree component, and using the fact that the length of an Artinian ring is the same as that of its injective hull, we transform this into a question about rings of the form $k[x_1,\dots,x_n]/(x_1^{d_1}, \dots, x_n^{d_n})$ and the annihilator of $x_1 + \dots + x_n$ therein. We in particular use refinements of functions introduced by Han and Monsky. This was motivated by questions about behavior of the length of local cohomology with support in the maximal ideal of thickenings, that is, $R/I^t$ as $t$ grows. This project is joint work with Mel Hochster.
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03:00 PM  03:05 PM


Group Photo

 Location
 SLMath: Front Courtyard
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 Abstract
 
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03:00 PM  03:30 PM


Afternoon Tea

 Location
 SLMath: Atrium
 Video


 Abstract
 
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03:30 PM  04:30 PM


Multiplicity Free Prime Ideals are Glicci
Elisa Gorla (Université de Neuchâtel)

 Location
 SLMath: Eisenbud Auditorium, Online/Virtual
 Video

 Abstract
A central question in Gorenstein liaison asks whether every CohenMacaulay ideal is glicci, i.e., whether every CohenMacaulay ideal belongs to the Gorenstein liaison class of a complete intersection. After introducing Gorenstein liaison and motivating this question, I will report on a joint work with Rajchgot and Satriano, where we show that every multiplicityfree prime ideal is glicci.
 Supplements



04:30 PM  05:30 PM


Panel Discussion
Haydee Lindo (Harvey Mudd College), Rebecca R.G. (George Mason University), Liana Sega (University of Missouri Kansas City), Hema Srinivasan (University of Missouri), Sarah Witherspoon (Texas A & M University)

 Location
 SLMath: Commons Room
 Video


 Abstract
Moderator: Hema Srinivasan, University of Missouri
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06:00 PM  08:00 PM


Dinner

 Location
 
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