Graham Denham (U Western Ontario) 10:00-10:55am (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) 11:30am-12:30pm (location: MATH 175)

Title:
The Elekes-Szab\'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          12:30-2:00pm (individual, off campus)

Eric Katz (Ohio State U) 2:00-3:00pm(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 Log-concavity
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 log-concavity 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    3:00-4:00pm (location: next to MATH 175)

JM Landsberg (Texas A&M)   4:00-5:00pm (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^{n-1} n-th 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 n-1 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.

Dinner: Saturday eveing at 6:30pm.  The dinner will be at

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SUNDAY, October 23

Coffee and pastries          8:30-9:30am  (location MATH library, 3rd floor of MATH building)

Richard Hain (Duke U)   9:30-10:30 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 non-zero
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 10:30-11:00 AM (location: next to MATH 175)

Mihnea Popa (Northwestern)   11:00-12:00 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).

Please note that Saturday morning is the Purdue Half-marathon http://purduehalf.com/ which will create some roadclosures (http://purduehalf.com/participant-information.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:

* the Hilton Garden Inn

* the  Campus Inn

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.