## Infinite Generaton of Non-Cocompact Lattices on Right-Angled Buildings

SPECIAL LECTURE

Anne Thomas

University of Sydney, NSW

April 6, 2011

SPECIAL LECTURE

Menachem Kojman

Ben Gurion University of the Negev; Member, School of Mathemtics

April 6, 2011

**MATHEMATICAL CONVERSATIONS**

"We know that God exists because mathematics is consistent and we know that the devil exists because we cannot prove the consistency." -- Andre Weil

Phillip Griffiths

Professor Emeritus, School of Mathematics

April 6, 2011

Ashwin Nayak

University of Waterloo

April 4, 2011

Recursive Majority-of-three (3-Maj) is a deceptively simple problem in the study of randomized decision tree complexity. The precise complexity of this problem is unknown, while that of the similarly defined Recursive NAND tree is completely understood.

Alvaro Pelayo

Member, School of Mathematics

April 4, 2011

Suh-Hyun Choi

Korea Advanced Institute of Science and Technology (KAIST)

March 31, 2011

Elena Fuchs

Institute for Advanced Study

March 30, 2011

Fred Diamond

Brandeis University

March 30, 2011

Grant Schoenbeck

Princeton University

March 29, 2011

In this talk, I will give new proofs for the hardness amplification of fficiently samplable predicates and of weakly verifiable puzzles. More oncretely, in the first part of the talk, I will give a new proof of Yao's XOR-Lemma as well as related theorems in the cryptographic setting. This proof seems simpler than previous ones, yet immediately generalizes to statements similar in spirit such as the extraction lemma used to obtain pseudo-random generators from one-way functions [Hastad, Impagliazzo, Levin, Luby, SIAM J. on Comp. 1999].

Institute for Advanced Study

March 29, 2011