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SUMMARY:Federico Ardila (San Francisco State University)
DTSTART:20240306T170000Z
DTEND:20240306T180000Z
DTSTAMP:20260422T225823Z
UID:CG-BLT/1
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CG-BLT/1/">I
 ntersection theory of matroids: variations on a theme</a>\nby Federico Ard
 ila (San Francisco State University) as part of Combinatorics and Geometry
  BLT Seminar\n\n\nAbstract\nChow rings of toric varieties\, which originat
 e in intersection theory\, feature a rich combinatorial structure of indep
 endent interest. We survey four different ways of computing in these rings
 \, due to Billera\, Brion\, Fulton–Sturmfels\, and Allermann–Rau. We i
 llustrate the beauty and power of these methods by sketching four proofs o
 f Huh and Huh–Katz’s formula µ^k (M) = deg(α^{r−k}β^k) for the co
 efficients of the reduced characteristic polynomial of a matroid M as the 
 mixed intersection numbers of the hyperplane and reciprocal hyperplane cla
 sses α and β in the Chow ring of M. Each of these proofs sheds light on 
 a different aspect of matroid combinatorics\, and provides a framework for
  further developments in the intersection theory of matroids. \n\nOur pres
 entation is combinatorial\, and does not assume previous knowledge of tori
 c varieties\, Chow rings\, or intersection theory.\n
LOCATION:https://researchseminars.org/talk/CG-BLT/1/
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BEGIN:VEVENT
SUMMARY:Diane Maclagan (University of Warwick)
DTSTART:20240403T160000Z
DTEND:20240403T170000Z
DTSTAMP:20260422T225823Z
UID:CG-BLT/2
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CG-BLT/2/">T
 ropical Schemes</a>\nby Diane Maclagan (University of Warwick) as part of 
 Combinatorics and Geometry BLT Seminar\n\n\nAbstract\nThe tropicalization 
 of a subscheme of P^n is given by a homogeneous ideal in the semiring of t
 ropical polynomials that satisfies some matroidal conditions.  This can be
  thought of as a "tower of valuated matroids".  In this talk I will highli
 ght what we currently know about the connection between these matroids and
  the geometry of the subscheme\, including recent progress on the Nullstel
 lensatz with Felipe Rincon\, and some connections still to be understood.\
 n
LOCATION:https://researchseminars.org/talk/CG-BLT/2/
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BEGIN:VEVENT
SUMMARY:Nicholas Proudfoot (University of Oregon)
DTSTART:20240501T160000Z
DTEND:20240501T170000Z
DTSTAMP:20260422T225823Z
UID:CG-BLT/3
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CG-BLT/3/">C
 ategorical valuations for polytopes and matroids</a>\nby Nicholas Proudfoo
 t (University of Oregon) as part of Combinatorics and Geometry BLT Seminar
 \n\n\nAbstract\nValuations of matroids are very useful and very mysterious
 .  After taking some time to explain this concept\, I will categorify it\,
  with the aim of making it both more useful and less mysterious.\n
LOCATION:https://researchseminars.org/talk/CG-BLT/3/
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BEGIN:VEVENT
SUMMARY:Alex Fink (Queen Mary University of London)
DTSTART:20240605T160000Z
DTEND:20240605T170000Z
DTSTAMP:20260422T225823Z
UID:CG-BLT/4
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CG-BLT/4/">S
 peyer's g conjecture and Betti numbers for a pair of matroids</a>\nby Alex
  Fink (Queen Mary University of London) as part of Combinatorics and Geome
 try BLT Seminar\n\n\nAbstract\nIn 2009\, looking to bound the face vectors
  of matroid subdivisions and tropical linear spaces\, Speyer introduced th
 e g-invariant of a matroid. He proved its coefficients nonnegative for mat
 roids 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 Berget that
  proves the conjecture.\n\nGeometrically\, the main ingredient is a variet
 y obtained from projection away from the base of the matroid tautological 
 vector bundles of Berget--Eur--Spink--Tseng\, and its initial degeneration
 s. Combinatorially\, it is an extension of the definition of external acti
 vity to a pair of matroids and a way to compute it using the fan displacem
 ent 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://researchseminars.org/talk/CG-BLT/4/
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BEGIN:VEVENT
SUMMARY:Cynthia Vinzant (University of Washington)
DTSTART:20240703T160000Z
DTEND:20240703T170000Z
DTSTAMP:20260422T225823Z
UID:CG-BLT/5
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CG-BLT/5/">T
 ropicalization of Principal Minors</a>\nby Cynthia Vinzant (University of 
 Washington) as part of Combinatorics and Geometry BLT Seminar\n\n\nAbstrac
 t\nTropicalization is a way to understand the asymptotic behavior of algeb
 raic (or semi-algebraic) sets through polyhedral geometry. In this talk\, 
 I will describe the tropicalization of the principal minors of real symmet
 ric and Hermitian matrices. This gives a combinatorial way of understandin
 g their asymptotic behavior and discovering new inequalities on these mino
 rs. For positive semidefinite matrices\, the resulting tropicalization wil
 l have a nice combinatorial structure called M-concavity and be closely re
 lated to the tropical Grassmannian and tropical flag variety. For general 
 Hermitian matrices\, this story extends to valuated delta matroids.\n\nThi
 s is based on joint works with Abeer Al Ahmadieh\, Nathan Cheung\, Tracy C
 hin\, Gaku Liu\, Felipe Rincón\, and Josephine Yu.\n
LOCATION:https://researchseminars.org/talk/CG-BLT/5/
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