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Student/Postdoc Working Geometry Seminar

The seminar meets Mondays at 5pm in Blocker 628.

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	Date Time	Location	Speaker	Title – click for abstract
	01/13 4:00pm	BLOC 302	JM Landsberg	*Introduction to sheaves and sheaf cohomology* This will be the first in a series of lectures. An outline is as follows: sheaf cohomology via Cech (GH=Griffiths-Harris 0.3) sheaves on P^n - cohomology and dictionary with modules (e.g. Hartshorne p225) spectral sequences and hypercohomology (GH 438-454) Belinson theorem (Okonek-Spindler-Schneider p239-246) application to spaces of matrices of constant rank
	01/27 4:00pm	BLOC 302	JM Landsberg Texas A&M	*Modules over the polynomial ring and sheaves on projective space: the dictionary and examples*
	02/10 4:00pm	BLOC 302	T. Mandziuk	*Introduction to spectral sequences (following Griffiths-Harris)*
	02/17 4:00pm	BLOC 302	T. Mandziuk Texas A&M	*Introduction to spectral sequences cont'd*
	02/24 4:00pm	BLOC 302	Derek Wu Texas A&M	*Hypercohomology (following Griffiths-Harris)*
	03/03 4:00pm	BLOC 302	Derek Wu Texas A&M	*Hypercohomology II*
	03/05 3:00pm	BLOC 306	R. Oliveira	*Permanents and stuff*
	03/17 4:00pm	BLOC 302	H. Huang Texas A&M	*Cohomology of the monad II*
	03/21 5:00pm	BLOC 302	Yevgeniya Tarasova Univedrsity of Michigan	*An introduction to liaison*
	03/24 4:00pm	BLOC 302	JM Landsberg Texas A&M	*Why study vector bundles on projective space?* I will explain two motivations for studying vector bundles on projective space: Hartshorne's conjecture on complete intersections and spaces of matrices of constant rank.
	03/31 4:00pm	BLOC 302	H. Huang Texas A&M	*Spaces of constant rank, after Boralevi et. al. I*
	04/07 4:00pm	BLOC 302	H. Huang Texas A&M	*Spaces of const. rank after Boralevi et. al. cont'd*
	04/14 4:00pm	BLOC 302	JM Landsberg Texas A&M	*Geometry of Instanton bundles.* This will be independent of previous lectures. I will explain instanton bundles on P^3 and how to construct them from geometric data following parts of MR0514430 - Stable vector bundles of rank 2 on P3 Hartshorne, Robin Math. Ann. 238 (1978), no. 3, 229–280.
	04/21 4:00pm	BLOC 302	JM Landsberg Texas A&M	*Tensors of minimal border rank: structural results* I will describe recent work in progress with Gesmundo, Jelisiejew, and Mandzuik.
	04/28 4:00pm	BLOC 302	T. Mandziuk Texas A&M	*Border rank lower bounds via deformation theory*
	05/05 4:00pm	BLOC 302	JM Landsberg Texas A&M	*Elementary components of the Hilbert scheme, after Jelisiejew* I'll lecture from arXiv:1710.06124