Algebra, Geometry and Combinatorics Day (AlGeCom) is a one day,
informal meeting of mathematicians from UIUC, Purdue University, IUPUI, Loyola University Chicago , DePaul University, University of Notre Dame, and nearby universities, with interests in algebra,
geometry and combinatorics (widely interpreted).
Further details will be posted here as they become available. You may
contact the University of Illinois organizers
Hal Schenck and Alexander Yong, or the Purdue organizers
Uli Walther
and Saugata Basu or IUPUI organizer Evgeny Mukhin, or the Loyola organizer Peter Tingley or the DePaul organizer Chris Drupieski. Date: October 22 AND 23, 2016
Location: Department of Mathematics of Purdue University
Registration is free. To preregister, email the local organizer Uli Walther (walther@math.purdue.edu) by October 8, indicating whether you plan to participate in the poster session.
Limited travel support is available for graduate students. To apply, email Uli Walther (walther@math.purdue.edu) by September 15 with: the name of your university, the name of your advisor, a summary of your research interests, a summary of your anticipated travel expenses, and whether you plan to participate in the poster session. Funding decisions will be made by September 25.
For a map, click here. The math building is nameless on this map, it is the one that is to the SouthEast of HAAS Hall, and to the NorthEast of BRNG Hall, and to the West of CL50. Morning coffee/refreshments will be in the MATH library. The library is on the 3rd floor of the MATH building.
All talks will be in MATH 175, at the foot of the MATH building opposite the elevators (North side of the "breezeway").
Poster session and afternoon tea will be in the atrium next to MA175.
The best place to park: Weekend parking is available in the parking lot next to the MATH building, Northwest from the MATH building across University Street. If you are driving, bring a GPS and some time. Many streets on campus are 1way and there is a lot of construction.
Speakers and schedule:
SATURDAY, October 22
Coffee and pastries 910am (location: MATH library, MATH building 3rd floor)
Graham Denham (U Western Ontario) 10:0010:55am (location: MATH 175)
Title: Gysin models for matroids
Abstract. In favourable conditions, the Leray spectral sequence gives a model, in the sense of rational homotopy theory, for a hypersurface complement in a smooth complex variety. I will describe how this works for affine, toric and elliptic hyperplane arrangements: one obtains a bigraded differential algebra which captures both the cohomology of the complement and of a choice of compactification. The notion of a combinatorial blowup, due to Feichtner and Kozlov (2004), makes it possible to extend the construction for linear arrangements to all matroids, regardless of realizability. This is based on joint work with Christin Bibby and Eva Feichtner.
Refreshments between talks (location: next to MATH 175)
Orit Raz (IAS) 11:30am12:30pm (location: MATH 175)
Title: The ElekesSzab\'o problem and applications to combinatorial geometry
Abstract: Let F(x,y,z) be a real trivariate polynomial of constant degree, and let A,B,C be three sets of real numbers, each of size n. How many points of A x B x C can lie on {F=0}? This question has been studied by Elekes and R\'onyai and then by Elekes and Szab\'o about 15 years ago.
In the talk I will review some recent results concerning this problem and its variants, and introduce some applications of the results to problems in extremal combinatorial geometry.
Lunch 12:302:00pm (individual, off campus)
Eric Katz (Ohio State U) 2:003:00pm(location: MATH 175)
Title: Hodge Theory in Combinatorics
Abstract: We discuss applications of Hodge theory which is a part of algebraic geometry to problems in combinatorics, in particular to Rota's Logconcavity Conjecture. The conjecture was motivated by a question in enumerating proper colorings of a graph which are counted by the chromatic polynomial. This polynomial's coefficients were conjectured to form a unimodal sequence by Read in 1968. This conjecture was extended by Rota in his 1970 ICM address to assert the logconcavity of the characteristic polynomial of matroids which are the common combinatorial generalizations of graphs and linear subspaces. We discuss the resolution of this conjecture which is joint work with Karim Adiprasito and June Huh. The solution draws on ideas from the theory of algebraic varieties, specifically Hodge theory, showing how a question about graph theory leads to a solution involving Grothendieck's standard conjectures.
Coffee Break 3:004:00pm (location: next to MATH 175)
JM Landsberg (Texas A&M) 4:005:00pm (location: MATH 175)
Title: Optimality v. Symmetry
Abstract: Abstract: Given a polynomial or tensor with symmetry, does an optimal expression for it also have symmetry? A classical example is Fischer's expression for the monomial x_1x_2...x_n as a sum of 2^{n1} nth powers of linear forms. (Ranestad and Schreyer showed his expression is optimal.) The monomial is invariant under permutations of the basis vectors, the permutation group on n elements. Fischer's expression also has symmetry, but under the permutation group on n1 elements! I will discuss how to exploit such symmetry in two central problems in theoretical computer science: Valiant's algebraic analog of P v. NP and the problem of determining the number of arithmetic operations needed to multiply two nxn matrices. The first is a comparison of the permanent and determinant polynomials. The second became a question in 1969 when Strassen discovered the standard algorithm for multiplying matrices is not the optimal one, which, after much work, has led computer scientists to conjecture that as n grows, it becomes almost as easy to multiply nxn matrices as it is to add them!
The first project is joint work with N. Ressayre, the second is joint work with G. Ballard, L. Chiantini, C. Ikenmeyer, G. Ottaviani and N. Ryder.
Poster session and informal discussions: 5:156:00pm (location: atrium next to MATH 175))We will set up posters during the afternoon coffee break on Saturday.
Dinner: Saturday eveing at 6:30pm. The dinner will be at
India Mahal, 111 S River Rd, West Lafayette, IN.
This is the intersection of State and River Road. 15 minutes walk from the department.

SUNDAY, October 23
Coffee and pastries 8:309:30am (location MATH library, 3rd floor of MATH building) Richard Hain (Duke U) 9:3010:30 AM (location: MATH 175)
Title: Motivic Structures on Mapping Class Groups
Abstract: In this talk I will explain how much we know about motivic structures on (relative completions of) mapping class groups. Results of Harer and Ivanov imply that the fundamental cases are genus 0 with 4 or 5 marked points, and genus 1 with one point or one nonzero tangent vector. I will try to explain the genus 1 case and how it relates to higher genus. This is partly a report on joint work with Makoto Matsumoto on universal mixed elliptic motives and more recent work with Francis Brown.
Refreshements 10:3011:00 AM (location: next to MATH 175)
Mihnea Popa (Northwestern) 11:0012:00 AM (location: MATH 175)
Title: Hodge ideals
Abstract: I will present joint work with M. Mustata, in which we study a sequence of ideals arising naturally from M. Saito's Hodge filtration on the localization along a hypersurface. The multiplier ideal of the hypersurface appears as the first step in this sequence, which as a whole provides a more refined measure of singularities. We give applications to the comparison between the Hodge filtration and the pole order filtration, adjunction, and the singularities of hypersurfaces in projective space and theta divisors on abelian varieties.

Conference Dinner:Saturday eveing at 6:30pm. The dinner will be at India Mahal, 111 S River Rd, West Lafayette, IN. This is the intersection of State and River Road. 15 minutes walk from the department.

Local Organizer: Uli Walther (walther@math.purdue.edu)
Public Transportation: Unnecessary/not recommended.
Parking: Weekend parking is available in the parking lot next to the MATH building, Northwest from the MATH building across University Street. It is called "PGU" on the map above. Because of construction, it is not entirely trivial to get to the parking lot. It is recommended that you come along State Street (either through town if you come from I65, or from the corresponding US 231 exit) and then turn North onto University Street. (If you come on I65 from the North, take Exit 193 to US 231 South).
Here is a more official description:
Please note that Saturday morning is the Purdue Halfmarathon http://purduehalf.com/ which will create some roadclosures (http://purduehalf.com/participantinformation.html).
Lodging: Economical options: The UnionClub Hotel is holding a block of rooms under the group name "Algebra Day" at the rate of $125 per night (double), $99 per night (single) plus tax, for the nights of October 21 and 22. See here for reservation details. Attendees should book a room by calling the hotel directly and mentioning the group name "AlGeCom". NOTE: the hotel only promises to hold the block of rooms at the group rate through October 10. If the Union sells out, other options are:
Banquet: In order to plan it, please LET US KNOW if you plan to particiapte: send an email to walther@math.purduel.edu and indicate how many people will be in your party.

