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Lecturer 허준이
Dept. 미국 프린스턴대 교수, 한국 고등과학원 석학교수
date Jul 27, 2022

 

 

I will tell two interrelated stories illustrating fruitful interactions between combinatorics and Hodge theory. The first is that of Lorentzian polynomials, based on my joint work with Petter Brändén. They link continuous convex analysis and discrete convex analysis via tropical geometry, and they reveal subtle information on graphs, convex bodies, projective varieties, Potts model partition functions, log-concave polynomials, and highest weight representations of general linear groups. The second is that of intersection cohomology of matroids, based on my joint work with Tom Braden, Jacob Matherne, Nick Proudfoot, and Botong Wang. It shows a surprising parallel between the theory of convex polytopes, Coxeter groups, and matroids. After giving an overview of the similarity, I will outline proofs of two combinatorial conjectures on matroids, the nonnegativity conjecture for their Kazhdan-Lusztig coefficients and the top-heavy conjecture for the lattice of flats.
 
호지 구조와 조합론 사이의 상호작용을 보여주는 서로 밀접히 관련된 두 이야기를 들려드릴 계획이에요. 첫째는 해석과 조합을 잇는 로렌츠 다항식 이야기이고, 둘째는 기하와 조합을 잇는 매트로이드 교차 코호몰로지 이야기입니다. 선형 대수 이상의 수학에 익숙하신 분들께 추천해 드립니다.

 

Atachment
Attachment '1'
List of Articles
Category Subject Dept. Lecturer
Special Colloquia What is Weak KAM Theory? file ENS-Lyon Albert Fathi
Special Colloquia Regularity of solutions of Hamilton-Jacobi equation on a domain file ENS-Lyon Albert Fathi
Special Colloquia Queer Lie Superalgebras file Univ. of Texas, Arlington Dimitar Grantcharov
Special Colloquia Persistent Homology file Stanford University Gunnar E. Carlsson
Special Colloquia Structures on Persistence Barcodes and Generalized Persistence file Stanford University Gunnar E. Carlsson
Special Colloquia Topological Mapping of Point Cloud Data file Stanford University Gunnar E. Carlsson
Special Colloquia Contact topology and the three-body problem file 서울대학교 Otto van Koert
Special Colloquia Mathematical Analysis Models and Siumlations file Collège de France Pierre-Louis Lions
Special Colloquia Harmonic bundles and Toda lattices with opposite sign file RIMS, Kyoto Univ. Takuro Mochizuki
Special Colloquia Regularization by noise in nonlinear evolution equations file Dep. Math., Kyoto Univ. Yoshio Tsutsumi
Special Colloquia Irreducible Plane Curve Singularities file 서울대학교 강정혁
Special Colloquia Algebraic surfaces with minimal topological invariants file 고등과학원 금종해
Special Colloquia 최고과학기술인상수상 기념강연: On the wild world of 4-manifolds file 서울대학교 박종일
Special Colloquia A wrapped Fukaya category of knot complement and hyperbolic knot file 포항공대 오용근
Special Colloquia A New Approach to Discrete Logarithm with Auxiliary Inputs file 서울대학교 천정희
Special Colloquia Combinatorics and Hodge theory file 미국 프린스턴대 교수, 한국 고등과학원 석학교수 허준이
Special Colloquia 허준이 교수 호암상 수상 기념 강연 (Lorentzian Polynomials) file Professor, Stanford University 허준이 교수
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