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Extra Form
강연자 허준이
소속 미국 프린스턴대 교수, 한국 고등과학원 석학교수
date 2022-07-27

 

 

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
첨부 '1'
List of Articles
카테고리 제목 소속 강연자
수학강연회 Towards Trustworthy Scientific Machine Learning: Theory, Algorithms, and Applications file KAIST 신연종
수학강연회 Elliptic equations with singular drifts in critical spaces file 서강대학교 김현석
수학강연회 Contact topology of singularities and symplectic fillings file 순천대학교 권명기
BK21 FOUR Rookies Pitch 2022-2 Rookies Pitch: Representation Theory(이신명) file 수리과학부 이신명
BK21 FOUR Rookies Pitch 2022-2 Rookies Pitch: Representation Theory(허태혁) file QSMS 허태혁
BK21 FOUR Rookies Pitch 2022-2 Rookies Pitch: Harmonic Analysis (오세욱) file 고등과학원 오세욱
BK21 FOUR Rookies Pitch 2022-2 Rookies Pitch: Harmonic Analysis (함세헌) file 수학연구소 함세헌
특별강연 Combinatorics and Hodge theory file 미국 프린스턴대 교수, 한국 고등과학원 석학교수 허준이
BK21 FOUR Rookies Pitch 2022-1 Rookies Pitch: Harmonic Analysis (Kalachand Shuin) file BK21 Kalachand Shuin
BK21 FOUR Rookies Pitch 2022-1 Rookies Pitch:Functional Analysis (정민구) file 고등과학원 정민구
수학강연회 Regularity theory for non-autonomous elliptic equations in divergence form file 서강대학교 옥지훈
BK21 FOUR Rookies Pitch 2022-1 Rookies Pitch: Algebraic Topology (송종백) file 고등과학원 송종백
BK21 FOUR Rookies Pitch 2022-1 Rookies Pitch: Symplectic/Algebraic Geometry (좌동욱) file 고등과학원 좌동욱
수학강연회 <2020년도 젊은 과학자상 수상 기념강연> Metastability of stochastic systems file 서울대학교 서인석
수학강연회 Geometric Langlands theory: A bridge between number theory and physics file 서울대학교 유필상
수학강연회 Noise-induced phenomena in stochastic heat equations file 포항공대 김건우
BK21 FOUR Rookies Pitch 2022-1 Rookies Pitch: Functional Analysis (Wang Xumin) file 수학연구소 Wang Xumin
BK21 FOUR Rookies Pitch 2022-1 Rookies Pitch: Probability, PDE (Ramil Mouad) file 수학연구소 Ramil Mouad
수학강연회 Mirror symmetry of pairings file 숭실대학교 이상욱
BK21 FOUR Rookies Pitch 2022-1 Rookies Pitch: Geometric Group Dynamics (서동균) file 수학연구소 서동균
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