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Extra Form
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
Math Colloquia Partial differential equations with applications to biology file POSTECH 황형주
Math Colloquia Diophantine equations and moduli spaces with nonlinear symmetry file 서울대학교 황준호
Math Colloquia Symplectic Geometry, Mirror symmetry and Holomorphic Curves file 연세대 수학과 홍한솔
Math Colloquia Toward bridging a connection between machine learning and applied mathematics file 성균관대학교 홍영준
Math Colloquia 돈은 어떻게 우리 삶에 돈며들었는가? (불확실성 시대에 부는 선형적으로 증가하는가?) file 농협은행 홍순옥
Math Colloquia <학부생을 위한 ɛ 강연> Self-Supervised Learning in Computer Vision file 인하대학교 현윤석
Math Colloquia Limit computations in algebraic geometry and their complexity file POSTECH 현동훈
Math Colloquia Geometry, algebra and computation in moduli theory file 서울대 현동훈
Math Colloquia <학부생을 위한 ɛ 강연> Geometry and algebra of computational complexity file 서울대학교 현동훈
BK21 FOUR Rookies Pitch 2022-2 Rookies Pitch: Representation Theory(허태혁) file QSMS 허태혁
Math Colloquia Mechanization of proof: from 4-Color theorem to compiler verification file 서울대 컴퓨터공학부 허충길
Special Colloquia 허준이 교수 호암상 수상 기념 강연 (Lorentzian Polynomials) file Professor, Stanford University 허준이 교수
Special Colloquia Combinatorics and Hodge theory file 미국 프린스턴대 교수, 한국 고등과학원 석학교수 허준이
BK21 FOUR Rookies Pitch 2022-2 Rookies Pitch: Harmonic Analysis (함세헌) file 수학연구소 함세헌
Math Colloquia 젊은과학자상 수상기념강연: From particle to kinetic and hydrodynamic descriptions to flocking and synchronization file 서울대학교 하승열
Math Colloquia One and Two dimensional Coulomb Systems file 카이스트 폴정
Math Colloquia Seeded Ising Model for Human Iris Templates and Secure Distributed Iris Recognition file 서울대학교 최형인
BK21 FOUR Rookies Pitch 2023-2 Generative Model(최재웅) file KIAS AI 기초과학센터 최재웅
Math Colloquia 극소곡면의 등주부등식 file KIAS 최재경
Math Colloquia 원의 유리매개화에 관련된 수학 file 건국대학교 최인송
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