There are no seminars this week.

Location: ** Hill 705**

Date & time: Monday, 01 February 2016 at 2:00PM - 2:11PM

Karim Adiprasito, Hebrew University/IAS:

A conjecture of Read predicts that the coefficients of the chromaticpolynomial of any graph form a log-concave sequence. A relatedconjecture of Welsh predicts that the number of linearly independentsubsets of varying sizes form a log-concave sequence for anyconfiguration of vectors in a vector space. Both conjectures are specialcases of the famous Rota conjecture asserting the log-concavity of thecoefficients of the characteristic polynomial of any matroid.

The recent story of these problems starts in 2010, when June Huh provedRota's conjecture for the special case of a hyperplane arrangement byidentifying the Whitney coefficients with mixed multiplicities of itsJacobian ideal. It subsequently emerged that virtually all proofs wecould come up with for this case use nontrivial geometric facts aboutthe arrangement and~or Hodge theory for projective varieties, and themore general conjecture of Rota for possibly

onrealizable 'configurations~matroids remained open until recently.

I will discuss how to extend Hodge theory beyond the classical settingto general matroids, starting with the surprising joint work withBjorner on Lefschetz theorems for Mikhalkin's p,q-groups, and thendiscuss the proof of the 'Kahler package' for general matroidal fans,which proves the Rota and Welsh conjecture in full generality. Allproofs are purely combinatorial, and do not rely on analytifications orprojective algebraic geometry, although there are some useful relationsI will mention.

Based on joint work with Anders Bjorner and with June Huh and Eric Katz'

Arthur Wang Organizer's Page

Charles Weibel Organizer's Page

Brooke Logan

Wujun Zhang, Rick Falk Organizer's Page

Xiaojun Huang, Jian Song, Sagun Chanillo

Pranjal Awasthi, Shubhangi Saraf Organizer's Page

Jeffry Kahn, Bhargav Narayanan, Abigail Raz Organizer's Page

Bryan Ek, Doron Zeilbrger Organizer's Page

- Paul Feehan, Manousos Maridakis, Natasa Sesum
Jason Saied, Corrine Yap Organizer's Page

Erik De Amorim Organizer's Page

Yonah Biers-Ariel Organizer's Page

Katie McKeon Organizer's Page

Yanyan Li, Zheng-Chao Han, Jian Song, Natasa Sesum

Lisa Carbone, Yi-Zhi Huang, James Lepowsky, Siddhartha Sahi Organizer's page

Grigor Sargsyan, Rebecca Coulsen Organizer's Page

Paul Feehan, Kihun Nam, Daniel Ocone, Triet Pham Organizer's page

Joel Lebowitz, Michael Kiessling

Yanyan Li, Haim Brezis

Matthew C Welsh

Stephen D. Miller, John C. Miller, Alex V. Kontorovich

Stephen D. Miller

Matthew Charnley Organizer's Page

Feng Luo, Xiaochun Rong, Hongbin Sun Organizer's page

Alejandro Ginory Organizer's Page

Borisov, Diaconescu, Tarasca, Woodward

Organizer: Vladimir Retakh Organizer's page

Claire Burrin, Amita Malik, Kei Nakamura

M. Lienert

- Show events from all categories

Directions: map and driving directions. If you need information on public transportation, you may want to check the New Jersey Transit page.

*Unfortunately, cancellations do occur from time to time. Feel free to call our department: 848-445-6969 before embarking on your journey. Thank you.*

Department of Mathematics
Rutgers University Hill Center - Busch Campus 110 Frelinghuysen Road Piscataway, NJ 08854-8019, USA Phone: +1.848.445.2390 Fax: +1.732.445.5530 |