Fall 2017

 

              FRAGMENT


Colorado State University
Department of Mathematics
Thursdays 3-5pm, Weber 201

 University of Colorado at Boulder
Department of Mathematics
Tuesdays 3-5pm, Math 350

  

This is a seminar series intended to involve people in the Front Range interested in Algebra, GeoMEtry and Number Theory. The seminar will meet either at CSU (green) or at CU Boulder (gold).

For more information, or to provide a speaker, contact Renzo, renzo AT math.colostate.edu, or Yano, casa AT math.colorado.edu.


Schedule of Talks:

 Date   Speaker  Location  Title
Aug 31Damiano Fulghesu
(MSU  Moorhead/CSU)    
 CSUFrom Classical to Equivariant Intersection Theory.
Sep 7
Vance Blankers
(CSU)
 CSU How to cope with a grumpy adviser +
The recursive structure of hyperelliptic loci in moduli spaces of curves

Sep 28Fumitoshi Sato
(U.Utah)
 CSUTalk 1. A construction of Moduli Spaces of Pointed Rational Curves
Talk 2. Topological recursion relations via degree 2 maps
Oct 5
 Linda Chen
(Swarthmore U)
 CSU Brill-Noether theory and determinantal formulas for degeneracy loci
Oct 12 Nicolas Addington    
 (U. of Oregon)
 CSU Complete intersections of unequal degrees
Oct 19    
Yunfeng Jiang
(U. Kansas)
 CSU TBA
Nov 2Dan Edidin    
(U. Missouri)
 CSU     TBA
Nov 9 Yuan Liu
(U Wisconsin)    
CSU     TBA
Nov 16Dhruv Ranganathan
(MIT)
 CSU     TBA
TBA

David Zureick-Brown
(Emory)    
CSU
 TBA

Have the dates show up in your calendar automatically: 

https://www.google.com/calendar/ical/4bddiire4eapkjuomee1p3l2k0%40group.calendar.google.com/public/basic.ics


Abstracts:

Damiano Fulghesu:  From Classical to Equivariant Intersection Theory.

Abstract: The main goal of this expository talk is to give a short introduction to equivariant intersection theory as it has been developed by B. Totaro, D. Edidin, and W. Graham. 

We will start from recalling some basic facts from classical intersection theory and explain how they generalize in the equivariant world.

We will also discuss some of the fundamental examples such as projective spaces, grassmannians, and moduli spaces of curves.

Graduate students are particularly welcome to participate.


Vance Blankers: The recursive structure of hyperelliptic loci in moduli spaces of curves


Abstract:  Moduli spaces of curves and their tautological rings enjoy a rich recursive combinatorial structure, which we describe in some detail. We then define a more generalized hyperelliptic locus \Hyp_{g,\ell,2m,n} in \Moduli_{g,\ell+2m+n}, requiring our hyperelliptic curves to have \ell marked Weierstrass points, m marked conjugate pairs, and n marked free points. Under the natural forgetful morphisms, these loci form a doubly-infinite family of tautological classes with its own recursive structure, which allows us to use an induction argument to show that any hyperelliptic class in genus two is extremal and rigid in the effective cone of codimension-(\ell+m) classes. Our main result extends work of Chen and Tarasca, who previously considered only Weierstrass point markings, and points towards a possible CohFT-like structure for hyperelliptic classes.


Fumitoshi Sato:  A construction of Moduli Spaces of Pointed Rational Curves/ Topological recursion relations via degree 2 maps


In the first hour I will explain a (new?) construction of moduli spaces of pointed rational curves as a wonderful compactification of a product of projective lines. In the second hour, the talk will turn to studying tautological classes in the moduli spaces of curves.

Mumford started to study enumerative geometry of moduli of curves.  I will give some generalizations of Mumford result.


Linda Chen: Brill-Noether theory and determinantal formulas for degeneracy loci 


I will begin with an overview of degeneracy loci and applications to the Brill-Noether theory of special divisors, and then describe recent developments in Schubert calculus, including K-theoretic formulas for degeneracy loci and K-classes of Brill-Noether loci. These recover the formulas of Eisenbud-Harris, Pirola, and Chan-López-Pflueger-Teixidor for Brill-Noether curves. This is joint work with Dave Anderson and Nicola Tarasca.


Nicolas Addington: Complete intersections of unequal degrees

Abstract
For a Fano hypersurface in P^n, the derived category decomposes into an exceptional collection and a category of matrix factorizations. For a complete intersection of k hypersurfaces of degree d, it decomposes into an exceptional collection and a sort of bundle of categories of matrix factorizations over P^{k-1}. What about a complete intersection of hypersurfaces of unequal degrees d_1...d_k? Do we get a similar bundle over weighted P^{k-1}, with weights d_1...d_k? Not really: it is better to view it as a categorical resolution of the category of matrix factorizations of some higher-dimensional, singular hypersurface. The prototypical example is Kuznetsov's degree-6 K3 surface resolving the category of matrix factorizations of a nodal cubic 4-fold. We will discuss several other examples and state some general results. This is joint work with Paul Aspinwall.






In previous semesters the seminar page was maintained by Renzo Cavalieri, Rachel Pries, Jeff Achter and Yano Casalaina. You can find the Fall 09 page here, Spring 10 here, Fall 10 here , Spring 11 here, Fall 11 here, Spring 12 here,  Fall 12 here,  Spring 2013.  For more recent semesters, see the side bar above.



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