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When: Monday or Wednesday @ 2pm

Where: Math 1311

Archives: 2011 | 2012 | 2013 | 2014 | 2015 | 2016

• #### Speaker: Organizational meeting (ANT and Lie Theory - Representation Theory) -

When: Wed, August 31, 2016 - 2:00pm
Where: Kirwan Hall 1311
• #### Speaker: Hilaf Hasson (UMD) -

When: Mon, September 12, 2016 - 2:00pm
Where: Kirwan Hall 1311

### View Abstract

Abstract: I will be describing a joint work with Ryan Eberhart. It is a well known fact that for every finite group G, there exists a G-Galois branched cover of P^1_K for some number field K. Given such a cover, Hilbert Irreducibility tells us that there are infinitely many G-Galois field extensions of K that arise as specializations. We will be asking variants of the question: under what conditions is one of these specializations isomorphic to the compositum of K with a G-Galois field extension of Q?"

• #### Speaker: Jonathan Rosenberg (UMD) - http://www2.math.umd.edu/~jmr

When: Wed, September 14, 2016 - 2:00pm
Where: Kirwan Hall 1311

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Abstract: I will explain a problem about duality for real elliptic curves and how it was motivated by physics, and how the result fits with work of Caldararu and Antieau.
• #### Speaker: Amin Gholampour (UMD) - http://www2.math.umd.edu/~amingh/

When: Mon, September 19, 2016 - 2:00pm
Where: Kirwan Hall 1311

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Abstract: Carlsson-Okounkov expressed the Chern classes of certain natural K-theory classes over the product of two Hilbert scheme of points on nonsingular surface in terms of Nakajima operators. As an application, taking the trace, they obtain a closed formula for the Euler class of the twisted tangent bundle of the Hilbert scheme generalizing Gottsche's formula.
We study certain top intersection products on the Hilbert scheme of points on a nonsingular surface relative to an effective smooth divisor. We find a formula relating these numbers to the corresponding intersection numbers on the absolute Hilbert schemes. In particular, we obtain a relative version of the formula found by Carlsson and Okounkov. If time permits, we discuss the relation of this to some virtual integrations over the nested Hilbert scheme of points on nonsingular surfaces as well as to some Donaldson-Thomas invariants of threefolds.
This is a joint work with Artan Sheshmani.
• #### Speaker: David Carchedi (George Mason) - http://math.gmu.edu/~dcarched/

When: Mon, September 26, 2016 - 2:00pm
Where: Kirwan Hall 1311

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Abstract: Etale homotopy theory, as originally introduced by Artin and Mazur in the late 60s, is a way of associating to a suitably nice scheme a pro-object in the homotopy category of spaces, and can be used as a tool to extract topological invariants of the scheme in question. It is a celebrated theorem of theirs that, after profinite completion, the etale homotopy type of an algebraic variety of finite type over the complex numbers agrees with the homotopy type of its underlying topological space equipped with the analytic topology. We will present work of ours which offers a refinement of this construction which produces a pro-object in the infinity-category of spaces (rather than its homotopy category) and applies to a much broader class of objects, including all algebraic stacks. We will also present a generalization of the previously mentioned theorem of Artin-Mazur, which holds in much greater generality than the original result.
• #### Speaker: Amin Gholampour (UMD) - http://www2.math.umd.edu/~amingh/

When: Mon, October 3, 2016 - 2:00pm
Where: Kirwan Hall 1311

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Abstract: We construct natural virtual fundamental classes for nested Hilbert schemes (of points and curves) of a nonsingular projective surface S. This allows us to define new invariants of S that recover some of the known important cases such as Poincare invariants (algebraic Seiberg-Witten invariants) of Durr-Kabanov-Okonek and the stable pair invariants of Kool-Thomas. In the case of the nested Hilbert scheme of points, we can express some of our invariants in terms of integrals over the products of Hilbert scheme of points on S, and relate them to the vertex operator formulas found by Carlsson-Okounkov. When the canonical line bundle K of S is positive, in combination with Mochizuki's formulas, we are able to express certain equivariant Donaldson-Thomas invariants of stable 2-dimensional sheaves on the total space of K in terms of our invariants of the nested Hilbert schemes, Seiberg-Witten invariants of S, and the integrals over the products of Hilbert scheme of points on S. This is a joint work with Artan Sheshmani and Shing-Tung Yau.
• #### Speaker: Jeff Achter (Colorado State University) - http://www.math.colostate.edu/~achter/

When: Wed, November 9, 2016 - 2:00pm
Where: Kirwan Hall 1311
• #### Speaker: Matthew Sattriano (Waterloo) - https://uwaterloo.ca/pure-mathematics/people-profiles/matthew-satriano

When: Mon, November 14, 2016 - 2:00pm
Where: Kirwan Hall 1311

### View Abstract

Abstract: Let X be a variety defined over an algebraically closed field of characteristic 0 and let \phi\colon X\to X be a birational automorphism. The Medvedev-Scanlon conjecture predicts when there is a rational point of X with dense orbit under \phi. We prove their conjecture in positive Kodaira dimension and then, contingent on conjectures in the Minimal Model Program, prove the conjecture for certain minimal threefolds of Kodaira dimension 0. This is joint work with Jason Bell, Dragos Ghioca, and Zinovy Reichstein.

• #### Speaker: Andre Chatzistamatiou (MPIM Bonn) -

When: Tue, November 22, 2016 - 1:00pm
Where: Kirwan Hall 1311

### View Abstract

Abstract: (Joint with M. Levine)
By a classical result of Roitman, a complete intersection $X$ of sufficiently small degree admits a rational decomposition of the diagonal. This means that some multiple of the diagonal by a positive integer $N$, when viewed as a cycle in the Chow group, has support in $X\times D\cup F\times X$, for some divisor $D$ and a finite set of closed points $F$. The minimal such $N$ is called the torsion order. We study lower bounds for the torsion order following the specialization method of Voisin, Colliot-Th\'el\`ene and Pirutka. We give a lower bound for the generic complete intersection with and without point. Moreover, we use methods of Koll\'ar and Totaro to show lower bounds for the very general complete intersection.