Algebra, Geometry and Combinatorics Day (AlGeCom)
Date of ALGECOMXVII: 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 AlgecomXVII): * 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 email 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) 7265400 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) 8630400 https://www.marriott.com/eventreservations/reservationlink.mi?id=1562769875586&key=GRP&app=resvlink Availability in this hotel is guaranteed if booked by Sept 6.
For the best places to park, see https://parking.wustl.edu/items/garageparking/
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 910am
1st Talk: Marcelo Aguiar (Cornell U) 1011am 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) 11:3012:30 Title: The ``generating function'' of orbit configuration spaces
Abstract: Given a finite group G acting freely on a space X, consider the space of ntuples of points in X whose Gorbits 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) 23pm Title: Gröbner geometry of Schubert polynomials through ice
Abstract. The cohomology ring of the flag variety is complicated and still not wellunderstood. Among our main tools are the Schubert polynomials of LascouxSchützenberger (1982). These polynomial representatives have a combinatorial "pipe dream" formula developed by BergeronBilley, FominKirillov, KnutsonMiller. The geometric naturality of Schubert polynomials and their pipe dream representations was established by KnutsonMiller (2005) via antidiagonal Gröbner degeneration of matrix Schubert varieties. We consider instead diagonal Gröbner degenerations. In this setting, KnutsonMillerYong (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 squareice model (recently rediscovered by LamLeeShimozono in the guise of "bumpless pipe dreams"). (Joint work with Zachary Hamaker and Anna Weigandt)
Poster session and afternoon tea 34pm
4th Talk: Sara Billey (U Washington) 4:155:15pm 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 $B_{n,n1}(X_n)$ 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 EdelmanGreene statistic

Parking:
Banquet: 6pm at Mandarin House (8004 Olive Blvd, Saint Louis, MO 63130, United States) This conference series is supported by the

