BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Federico Ardila (San Francisco State University)
DTSTART:20240306T170000Z
DTEND:20240306T180000Z
DTSTAMP:20260404T111245Z
UID:CG-BLT/1
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/CG-BL
 T/1/">Intersection theory of matroids: variations on a theme</a>\nby Feder
 ico Ardila (San Francisco State University) as part of Combinatorics and G
 eometry BLT Seminar\n\n\nAbstract\nChow rings of toric varieties\, which o
 riginate in intersection theory\, feature a rich combinatorial structure o
 f independent interest. We survey four different ways of computing in thes
 e rings\, due to Billera\, Brion\, Fulton–Sturmfels\, and Allermann–Ra
 u. We illustrate the beauty and power of these methods by sketching four p
 roofs of Huh and Huh–Katz’s formula µ^k (M) = deg(α^{r−k}β^k) for
  the coefficients of the reduced characteristic polynomial of a matroid M 
 as the mixed intersection numbers of the hyperplane and reciprocal hyperpl
 ane classes α and β in the Chow ring of M. Each of these proofs sheds li
 ght on a different aspect of matroid combinatorics\, and provides a framew
 ork for further developments in the intersection theory of matroids. \n\nO
 ur presentation is combinatorial\, and does not assume previous knowledge 
 of toric varieties\, Chow rings\, or intersection theory.\n
LOCATION:https://stable.researchseminars.org/talk/CG-BLT/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Diane Maclagan (University of Warwick)
DTSTART:20240403T160000Z
DTEND:20240403T170000Z
DTSTAMP:20260404T111245Z
UID:CG-BLT/2
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/CG-BL
 T/2/">Tropical Schemes</a>\nby Diane Maclagan (University of Warwick) as p
 art of Combinatorics and Geometry BLT Seminar\n\n\nAbstract\nThe tropicali
 zation of a subscheme of P^n is given by a homogeneous ideal in the semiri
 ng of tropical polynomials that satisfies some matroidal conditions.  This
  can be thought of as a "tower of valuated matroids".  In this talk I will
  highlight what we currently know about the connection between these matro
 ids and the geometry of the subscheme\, including recent progress on the N
 ullstellensatz with Felipe Rincon\, and some connections still to be under
 stood.\n
LOCATION:https://stable.researchseminars.org/talk/CG-BLT/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicholas Proudfoot (University of Oregon)
DTSTART:20240501T160000Z
DTEND:20240501T170000Z
DTSTAMP:20260404T111245Z
UID:CG-BLT/3
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/CG-BL
 T/3/">Categorical valuations for polytopes and matroids</a>\nby Nicholas P
 roudfoot (University of Oregon) as part of Combinatorics and Geometry BLT 
 Seminar\n\n\nAbstract\nValuations of matroids are very useful and very mys
 terious.  After taking some time to explain this concept\, I will categori
 fy it\, with the aim of making it both more useful and less mysterious.\n
LOCATION:https://stable.researchseminars.org/talk/CG-BLT/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alex Fink (Queen Mary University of London)
DTSTART:20240605T160000Z
DTEND:20240605T170000Z
DTSTAMP:20260404T111245Z
UID:CG-BLT/4
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/CG-BL
 T/4/">Speyer's g conjecture and Betti numbers for a pair of matroids</a>\n
 by Alex Fink (Queen Mary University of London) as part of Combinatorics an
 d Geometry BLT Seminar\n\n\nAbstract\nIn 2009\, looking to bound the face 
 vectors of matroid subdivisions and tropical linear spaces\, Speyer introd
 uced the g-invariant of a matroid. He proved its coefficients nonnegative 
 for matroids representable in characteristic zero and conjectured this in 
 general. Later\, Shaw and Speyer and I reduced the question to positivity 
 of the top coefficient. This talk will overview work in progress with Berg
 et that proves the conjecture.\n\nGeometrically\, the main ingredient is a
  variety obtained from projection away from the base of the matroid tautol
 ogical vector bundles of Berget--Eur--Spink--Tseng\, and its initial degen
 erations. Combinatorially\, it is an extension of the definition of extern
 al activity to a pair of matroids and a way to compute it using the fan di
 splacement rule. The work of Ardila and Boocher on the closure of a linear
  space in (P^1)^n is a special case.\n
LOCATION:https://stable.researchseminars.org/talk/CG-BLT/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cynthia Vinzant (University of Washington)
DTSTART:20240703T160000Z
DTEND:20240703T170000Z
DTSTAMP:20260404T111245Z
UID:CG-BLT/5
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/CG-BL
 T/5/">Tropicalization of Principal Minors</a>\nby Cynthia Vinzant (Univers
 ity of Washington) as part of Combinatorics and Geometry BLT Seminar\n\n\n
 Abstract\nTropicalization is a way to understand the asymptotic behavior o
 f algebraic (or semi-algebraic) sets through polyhedral geometry. In this 
 talk\, I will describe the tropicalization of the principal minors of real
  symmetric and Hermitian matrices. This gives a combinatorial way of under
 standing their asymptotic behavior and discovering new inequalities on the
 se minors. For positive semidefinite matrices\, the resulting tropicalizat
 ion will have a nice combinatorial structure called M-concavity and be clo
 sely related to the tropical Grassmannian and tropical flag variety. For g
 eneral Hermitian matrices\, this story extends to valuated delta matroids.
 \n\nThis is based on joint works with Abeer Al Ahmadieh\, Nathan Cheung\, 
 Tracy Chin\, Gaku Liu\, Felipe Rincón\, and Josephine Yu.\n
LOCATION:https://stable.researchseminars.org/talk/CG-BLT/5/
END:VEVENT
END:VCALENDAR