Midwest Algebraic Geometry Graduate Conference 2015

The Department of Mathematics, Statistics, and Computer Science at the University of Illinois at Chicago is pleased to host the Midwest Algebraic Geometry Graduate Conference for 2015.

The conference will feature nine talks beginning with the plenary lecture given at our departmental colloquium on Friday April 10th, followed by five talks on Saturday April 11th, and finishing with three talks on Sunday April 12th. The plenary talk will be given by Joe Harris of Harvard, and the talks on Saturday and Sunday will be given by graduate students in algebraic geometry.

The conference will take place at the University of Illinois, 851 South Morgan Street, Chicago, IL 60607 on April 10-12, 2015.

(This list does not update immediately.)

Limited funding for lodging and travel is available for both participants and speakers. If you'd like to be considered to speak, please register with the above link and submit an abstract to uicmaggc@gmail.com.

Graduate organizers for this event are: Seckin Adali, Tim Ryan, Alexander Stathis, and Xudong Zheng. The faculty organizer is Izzet Coskun.

If you have any questions, then please contact us at uicmaggc@gmail.com. Support provided by NSF RTG grant DMS-1246844.Schedule

Location | Event | ||

3:00 | LC C6 | Department Colloquium and Plenary LectureJoe Harris (Harvard) - TBA | |

4:15 | SEO 300 | Departmental Tea | |

5:30 | Dinner We will not provide dinner, but we will make reservations at a local restaurant for everyone who would like to attend. |

Location | Event | |

9:00 | SEO 300 | Breakfast We will provide coffee and assorted breakfast items. |

9:30 | LC C6 | Clemens Koppensteiner - A Microlocal Characterization of Perverse Coherent Sheaves |

10:45 | LC C6 | Eliana Duarte - Tensor Product Surfaces and Linear Syzygies |

12:00 | SEO 300 | Lunch Provided. |

1:30 | LC C6 | Ed Dewey - Characteristic Classes of Cameral Covers |

2:45 | LC C6 | David Bruce - Betti Tables of Graph Curves |

4:00 | LC C6 | Robert Walker - Uniform Bounds Lurking in Affine Toric Rings |

Location | Event | |

9:00 | SEO 300 | Breakfast We will provide coffee and assorted breakfast items. |

9:30 | LC C6 | Daniel Hast - The Geometry of "Short Intervals" in Function Field Arithmetic |

10:45 | LC C6 | Jake Levinson - Limit Linear Series and Real Schubert Calculus |

12:00 | LC C6 | Ashwath Rabindranath - Some Surfaces with Nonpolyhedral Nef Cones |

1:15 | SEO 300 | Lunch Provided. |

Map

Joe Harris - *Interpolation for Polynomials in Several Variables*Friday April 10th at 3:00pm

Clemens Koppensteiner - *A Microlocal Characterization of Perverse Coherent Sheaves*Saturday April 11th at 9:30am

Eliana Duarte - *Tensor Product Surfaces and Linear Syzygies*Saturday April 11th at 10:45am

Ed Dewey - *Characteristic Classes of Cameral Covers*Saturday April 11th at 1:30pm

Familes of operators generalize to certain gadgets called "Higgs Bundles" and spectral covers generalize to "cameral covers". Again there is a Hitchen map from one to the other, which has been useful for studying moduli spaces of principle bundles.

I will say a bit about the Hitchen map, and describe some work of Dima Arinkin and myself defining characteristic classes of cameral covers. The latter amounts to computing the cohomology ring of the moduli space of cameral covers and expressing its generators as Chern classes of certain natural vector bundles.

David Bruce - *Betti Tables of Graph Curves*Saturday April 11th at 2:45pm

Robert Walker - *Uniform Bounds Lurking in Affine Toric Rings*Saturday April 11th at 4:00pm

In structure, affine toric rings (coordinate rings of normal affine toric varieties) are "mused to be" the nicest class after regular rings on the one hand, and smooth rings on the other (since their singularities are rational). Starting from toric rings of dimension two or higher, I am searching for a result analogous to both ELS and the fact for smooth rings. The remainder of the talk will set up a statement of the conjecture I have in view, emphasizing work in progress to verify it in dimension two.

Daniel Hast - *The Geometry of "Short Intervals" in Function Field Arithmetic*Sunday April 12th at 9:30am

Jake Levinson - *Limit Linear Series and Real Schubert Calculus*Sunday April 12th at 10:45am

For genus 0 curves, this moduli space (call it $S$) turns out to be very well-behaved: for instance, it is flat and Cohen-Macaulay over $\overline{M_{0,n}}$, and has the correct (expected) relative dimension. Moreover, in the relative-dimension-zero case, recent work due to Mukhin-Tarasov-Varchenko (2007) and Speyer (2014) showed that the real locus of $S$ is actually an unramified covering space of $\overline{M_{0,n}}(\mathbb{R})$; the monodromy of the cover has an elegant description in terms of objects from classical (combinatorial) Schubert calculus.

I'll discuss this construction, and some recent analogous work concerning the case where $S$ has relative dimension 1. In this case, there is interesting structure to be seen in both the real and complex geometry of the fibers.

Ashwath Rabindranath - *Some Surfaces with Nonpolyhedral Nef Cones*Sunday April 12th at 12:00pm

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