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The meeting is planned twice a year, and the next iteration will take place at the University of Michigan at Ann Arbor on Saturday November 9, 2024. You and your students are invited to join us!.
Algecom Committee:
AlGeCom XXIIII Date: Saturday November 9, 2024
AlGeCom XXIIII Date: Saturday November 9, 2024
Location: East Hall, University of Michigan, Ann Arbor
Location: East Hall, University of Michigan, Ann Arbor
Campus map: https://campusinfo.umich.edu/campusmap
The speakers will be
Chris Eur (Carnegie Mellon University)
Patricia Klein (Texas A&M University)
Matt Larson (Princeton / Institute for Advanced Study)
Jianping Pan (Arizona State University)
Parking:
Parking:
TBD
Local Organizers (questions related to Algecom XXIII):
Local Organizers (questions related to Algecom XXIII):
David Speyer
ALGECOM is partially funded by a grant from the National Science Foundation, which provides limited support for students and postdocs to offset the cost of attendance. Everyone should apply by filling out the registration form below and indicating their interest in financial support (and we appreciate early applications). Funding decisions will be made shortly thereafter.
ALGECOM is partially funded by a grant from the National Science Foundation, which provides limited support for students and postdocs to offset the cost of attendance. Everyone should apply by filling out the registration form below and indicating their interest in financial support (and we appreciate early applications). Funding decisions will be made shortly thereafter.
There will also be a poster fair; you can sign up to present a poster!
There will also be a poster fair; you can sign up to present a poster!
We have already allocated much but not all of our financial support. Please seek out other sources of support if possible, but we will support some more attendees. Please fill out the registration form by October 15 to be considered for financial support. Please do fill out the form if you think you will come, even if you don't need support; it is helpful to us to know who will be coming.
Lodging:
Lodging:
A block of rooms has been reserved at Larkspur Landing , approximately four miles from East Hall. We encourage participants to arrange carpools from the hotel to campus. There is also a bus route, Route 23 , which runs every half hour on weekends. The closest stop to East Hall is the Central Campus Transit Center.
Guests can book reservations using this link: https://reservations.travelclick.com/9877616?groupID=4510108 and will be reimbursed if we have offered you support. Please book by October 8 to be sure of being included in the room block.
Tentative Schedule:
Tentative Schedule:
(All times are in the Eastern Time Zone)
Talks are in East Hall. Coffee in the Atrium.
9:00-9:30am Coffee and Registration
9:00-9:30am Coffee and Registration
9:30-10:30am Chris Eur (Carnegie Mellon University)
9:30-10:30am Chris Eur (Carnegie Mellon University)
Title: How do matroids behave like projective toric varieties?
Abstract: A tropical model of a matroid, called the Bergman fan, provides a toric variety whose Chow ring behaves like a smooth toric projective variety. What about sheaf cohomologies of line bundles or vector bundles? How should one make sense of such notions for a matroid? Even for linear matroids, many geometric questions remain. We discuss various developments surrounding these questions.
10:30-11:00am Break
10:30-11:00am Break
11:00-12:00am Matt Larson (Princeton/IAS)
11:00-12:00am Matt Larson (Princeton/IAS)
Title: Fine multidegrees and Grobner degenerations
Abstract: Grobner degenerations are a method for studying the geometry of a subvariety X of C^n using a scaling action of the multiplicative group C*, but they often lose a lot of information. This information loss can be minimized by compactifying affine space. We show that the possible Grobner degenerations of X are controlled by the homology class of the closure of X in (P^1)^n. This gives a simple criterion for a collection of squarefree polynomials to be a universal Grobner basis, which can be used to recover many known results on universal Grobner bases. We apply this result to a family of matrix Schubert varieties. Joint work with Daoji Huang.itle: Fine multidegrees and Grobner degenerations
12:00am-1:30pm Lunch
12:00am-1:30pm Lunch
1:30-2:30pm Patricia Klein (Texas A&M University)
1:30-2:30pm Patricia Klein (Texas A&M University)
Title: Gröbner degeneration in Schubert calculus
Abstract: Roughly speaking, enumerative geometry is a field whose goal is to count the "typical" number of solutions to certain types of families of polynomial equations, particularly when that number is finite. With a great deal of effort, especially in the wake of the work of Hermann Schubert around the turn of the 20th century, mathematicians made rigorous the notion of a "typical" answer and also made rigorous certain simplifying strategies Schubert had suggested. Indeed, making Schubert's arguments precise was the topic of Hilbert's 15th problem, and the field born from this study is now called Schubert calculus. The simplifications Schubert had suggested entail sliding or deforming the geometric objects to be studied while preserving the total number of whatever it is one wants to count. These strategies are what are now called degeneration techniques. In this talk, we will review some classical results in Schubert calculus, describe some modern questions in the area, and then explain how these questions are studied via Gröbner degeneration in particular.
2:30-3:00pm Break
2:30-3:00pm Break
3:00-4:00pm Jianpin Pang (Arizona State Univesity)
3:00-4:00pm Jianpin Pang (Arizona State Univesity)
Title: Variations of uncrowning algorithms and stable Grothendieck polynomials
Abstract: In this talk, I will provide the motivation, basic definitions, and abundant examples of tableaux related to variations of stable Grothendieck polynomials. The classic uncrowding algorithm defined by Buch on set-valued tableaux gives a bijective proof of Lenart’s Schur expansion for symmetric Grothendieck polynomials. Hook-valued tableaux are associated with stable canonical Grothendieck polynomials and we introduce an uncrowding algorithm on them. Recently Hwang, Jang, Kim, Song and Song gave a Schur expansion for the refined canonical stable Grothendieck polynomials (using exquisite tableaux). We discover a novel connection between the exquisite tableaux model and hook-valued tableaux via the uncrowding and jeu de taquin algorithms, using a classic result of Benkart, Sottile and Stroomer. This connection reveals a hidden symmetry of the hook-valued tableaux and the uncrowding algorithm defined on them. This talk is based on joint work with Pappe, Poh and Schilling, and with Jang, Kim, Pappe and Schilling.
4:00-5:00pm Poster Fair
5:00-??? Pizza
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