Algebra, Geometry and Combinatorics Day (AlGeCom)
Date of ALGECOM-XVII: September 21, 2019 Location: Department of Mathematics at Washington University at St. Louis
(Further details will be posted here as they become available)
Local Organizers (questions related to Algecom-XVII): * Martha Precup (Martha.precup@wustl.edu)
Registration: is free. To register, email the local organizer Laura Escobar at laurae@wustl.edu
If you are interested in presenting at the poster session, please e-mail Laura Escobar at laurae@wustl.eduThere may be some NSF support (hotel, airfare/car rental) for graduate students to attend.
Interested students should apply by sending to following information to Laura Escobar at laurae@wustl.edu by August 21, 2019.
1. Name:
2. Organization:
3. Will you be attending dinner?
4. Brief summary of research interests:
5. Research advisor:
6: Are you interested in presenting at the poster fair?
7. Approximate expenses:
Funding decisions will be made by August 31, 2019.
Lodging:
We have blocked 10 rooms each at the Clayton Plaza and the Sheraton in
Clayton. The reservation includes a complimentary full hot breakfast and
parking. To book a room follow the links below.
Clayton Plaza, $116
7750 Carondelet Ave, Clayton, MO 63105
Phone (314) 726-5400
https://reservations.travelclick.com/97426?RatePlanId=1726767
Use the code 1726767
Sheraton Plaza, $125 per night
7730 Bonhomme Ave, St. Louis, MO 63105
Phone: (314) 863-0400
https://www.marriott.com/event-reservations/reservation-link.mi?id=1562769875586&key=GRP&app=resvlink
Availability in this hotel is guaranteed if booked by Sept 6.
Speakers and schedule:
All talks will be in Wilson 214
Morning Coffee and pastries, Poster session, and afternoon tea will be
Cupples I Rooms 199 and 200
(See the map for locations)
Coffee and pastries 9-10am
1st Talk: Marcelo Aguiar (Cornell U) 10-11am Title: Mobius functions for real hyperplane arrangements
Abstract. We discuss a number of algebraic structures attached to a
real hyperplane arrangement, leading to the beginnings of a theory of noncommutative Mobius functions.
Background on hyperplane arrangement and Mobius functions will be reviewed.
The talk will contain geometric, combinatorial and algebraic aspects
and there will be many pictures. All based on joint work with Swapneel
Mahajan.
2nd Talk: Christin Bibby (U Michigan) 11:30-12:30 Title: The ``generating function'' of orbit configuration spaces
Abstract: Given a finite group G acting freely on a space X, consider the
space of n-tuples of points in X whose G-orbits are distinct. Letting n
vary, this yields a sequence of orbit configuration spaces. As
countless examples show, it can be fruitful to study a sequence of
complicated objects all at once via the formalism of generating functions. We apply this point of view
to the homology and combinatorics of orbit configuration
spaces: using the notion of twisted commutative algebras, which essentially
categorify exponential generating functions. With this idea, we will describe a factorization
of the orbit configuration space ``generating function'' into an infinite
product, whose terms are surprisingly easy to understand. Beyond the
intrinsic aesthetic of this decomposition and its quantitative consequences, it
encodes representation stability phenomena. This
is joint work with Nir Gadish.
3rd Talk: Oliver Pechenik (U Michigan) 2-3pm Title: Gröbner geometry of Schubert polynomials through ice
Abstract.
The cohomology ring of the flag variety is complicated and still not
well-understood. Among our main tools are the Schubert polynomials of
Lascoux-Schützenberger (1982). These polynomial representatives have a
combinatorial "pipe dream" formula developed by Bergeron-Billey,
Fomin-Kirillov, Knutson-Miller. The geometric naturality of Schubert
polynomials and their pipe dream representations was established by
Knutson-Miller (2005) via antidiagonal Gröbner degeneration of matrix
Schubert varieties. We consider instead diagonal Gröbner degenerations. In
this setting, Knutson-Miller-Yong (2009) obtained alternative combinatorics,
but only for the small class of vexillary matrix Schubert varieties. We
continue their program to a larger class, obtaining a neglected formula of
Lascoux (2002) in terms of the square-ice model (recently rediscovered by
Lam-Lee-Shimozono in the guise of "bumpless pipe dreams"). (Joint work with
Zachary Hamaker and Anna Weigandt)
Poster session and afternoon tea 3-4pm
4th Talk: Sara Billey (U Washington) 4:15-5:15pm Title: Boolean product polynomials, Schur positivity, and Chern plethysm
Abstract The Boolean product polynomial $B_{n,k}(X_n)$ is the product of
the linear forms $\sum_{i \in S} x_i$ where $S$ ranges over all $k$-element
subsets of $\{1, 2, \dots, n\}$. We prove that Boolean product polynomials
are Schur positive. We do this via a new method of proving Schur positivity
using vector bundles and a symmetric function operation we call Chern
plethysm. This gives a geometric method for producing a vast array of Schur
positive polynomials whose Schur positivity lacks (at present) a
combinatorial or representation theoretic proof. We relate the polynomials
$B_{n,k}(X_n)$ for certain $k$ to other combinatorial objects including
derangements, positroids, alternating sign matrices, and reverse flagged
fillings of a partition shape. We also relate $B_{n,n-1}(X_n)$ to a bigraded
action of the symmetric group $\symm_n$ on a divergence free quotient of
superspace. This talk is based on joint work with Lou Billera, Brendon
Rhoades, and Vasu Tewari.
Sunita Chepuri
Christian Gaetz: Separable elements in Weyl groups
Jaewoo Jung: Bounds on the regularity of quadratic monomial ideals
Jewell McMillon
Jodi McWhirter: Discrete Volumes of Coxeter Permutahedra
Kevin Marshall: Generalizations of Eavesdropping Games: Greedoids and Multiple Bugs
Erika Ordog: Canonical combinatorial minimal free resolutions of arbitrary monomial ideals
Isabel Perez: Spectra of Tropical Laplacians of Classical Root Polytopes
Colleen Robichaux: The ABCDs of Schubert Calculus
Gideon Orelowitz: Maximizing the Edelman--Greene statistic
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Parking:
Banquet: 6pm at Mandarin House (8004 Olive Blvd, Saint Louis, MO 63130, United States) This conference series is supported by the
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