* Jonah Blasiak (Drexel) 10:00-10:55am

Title:  Noncommutative Schur functions

Abstract: The theory of noncommutative Schur functions is an algebraic
approach to finding positive combinatorial formulae for the Schur expansions
of symmetric functions. It has its origins in the <i>plactic algebra</i>,
the free associative algebra in the alphabet of positive integers modulo
Knuth equivalence. It has been known since the work of Lascoux and
Schuetzenberger from the 1970's that the plactic algebra contains a
subalgebra isomorphic to the ring of symmetric functions, equipped with a
basis of noncommutative versions of Schur functions.
In the 1990's, Fomin and Greene generalized this by replacing certain pairs
of Knuth relations by weaker four-term relations. By studying the
noncommutative Schur functions in the algebra thus defined, they obtain
positive Schur expansions for a large class of
symmetric functions that includes the Stanley symmetric functions
and stable Grothendieck polynomials.
I will give an overview of recent developments of this theory, including
applications to Macdonald polynomials and Kronecker coefficients.
This is joint work with Sergey Fomin and Ricky Liu.



* Laura Escobar (UIUC) 11:30am-12:25pm

Title:  Toric matrix Schubert varieties

Abstract:  Start with a permutation matrix $\pi$ and consider all matrices that can be obtained from $\pi$ by taking downward row operations and rightward column
operations; the closure of this set gives the matrix Schubert variety $X_\pi$. Such a variety can be written as $X_\pi=Y_\pi\times \mathbb{C}^q$ (where
$q$ is maximal). We characterize when $Y_\pi$ is toric (with respect to a $(\mathbb{C}^*)^{2n-1}$-action) and study the associated polytope of its
projectivization. We construct regular triangulations of these polytopes which we show are geometric realizations of a family of subword complexes.
Based on joint work with Karola Mészáros.

* Joel Kamnitzer (Toronto) 2:00-2:55pm

Title: Monodromy of shift of argument eigenvectors and cactus groups

Abstract: For any semisimple Lie algebra, there is a family of maximal
commutative subalgebras of its universal envelopping algebras.  These
can be used to construct special bases of representations,
generalizing the Gelfand-Zetlin basis for gl_n.  By varying in this
family, we obtain an action of the cactus group on these bases.  This
action of the cactus group matches an action defined combinatorially
using crystals.

* Tri Lai  (IMA)   3:05-4:00pm

Title: Proof of a conjecture of Kenyon and Wilson on semicontiguous minors

Abstract: Kenyon and Wilson showed how to test if a circular planar electrical network is well-connected by checking the positivity of $n(n+1)/2$
central minors of the $n\times n$ response matrix (arXiv:1411.7425). Their test is based on the fact that any contiguous minor of a matrix can be
expressed as a Laurent polynomial in the central minors. Interestingly, the Laurent polynomial is the generating function of domino tilings of a
weighted Aztec diamond. They conjectured that any semicontiguous minor can also be written in terms of domino tilings of a region on the square
lattice. In this talk I will present a proof of the conjecture.

* Dinner: We do not have a subsidized banquet, but we will organize a group to
have dinner at Madras Masala. This is an excellent, inexpensive
($7-$15) and vegetarian friendly Indian restaurant. We will walk over from
East Hall at 5:45, or arrive there at 6.

Local Organizer: David Speyer (speyer@umich.edu)

Getting to Ann Arbor: The best airport to get to Ann Arbor is Detroit (DTW). You can get buses from the airport to Ann Arbor at http://michiganflyer.com/ costing $12 if reserved in advance or $15 if you walk on. Go to the Blake Transit Center, which is walkable to campus. A taxi will probably run about $60.

There are also several trains from Chicago and points west to Ann Arbor; check Amtrak for schedules.

Parking: The closest parking to East Hall is the garage on the corner of
Forest and South University, at $1.25/hour. Here is a local map, the conference is at East Hall on Church
Street.

Lodging: The Lamppost Inn is holding a block of rooms for the
nights of the 23rd and 24th under the name ALGECOM. Please make your own
reservations and let us know you have done so.

The Lamp Post Inn is 1.7 miles from East Hall. The conference will organize
carpools from the hotel to East Hall. For those who wish to drive
themselves, we will have information about parking options here soon. Bus
route 4 ( towards the department,  towards the hotel ) also goes near
both locations and runs every half hour on weekends (get off at Washtenaw
and South University and you will be two blocks from the math department),
but note that the last bus on Saturday is at 7 PM.

Childcare: Parents attending the conference and looking for childcare may
find care.com a useful reference.