# Joint Moments (Seminar)

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I will discuss recent progress concerning the joint moments of the characteristic polynomial of a random unitary matrix and its derivates, in the context of the connection between the Riemann zeta-function and random matrix theory.

# Random matrices and the Riemann zeta-function (Colloquium)

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I will review connections between random matrix theory and statistical properties of the Riemann zeta-function, including recent developments relating to extreme values of the zeta function on the critical line.

# Nonlocal minimal surfaces

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The theory of minimal surfaces in general Euclidean dimensions was developed in the 60's by De Giorgi, Reifenberg, Federer, Fleming, Almgren using measure theoretical methods. The approach due to De Giorgi is to interpret surfaces as boundaries of measurable sets E, and view the surface area as the perimeter of E which is defined as the BV norm of its characteristic function. A decade ago, we introduced with Caffarelli and Roquejoffre a nonlocal version of the perimeter functional which is relevant in the theory of phase-transitions with long-range interactions. In my lecture I will give an overview of the theory of the nonlocal minimal surfaces and discuss some of the more recent developments.

# Public Lecture: Cryptography in the Vietnam War

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One would assume that during the French and American wars in Vietnam, the impoverished guerrillas of the Viet Minh and NLF must have been badly outmatched on the purely technical side of warfare, including cryptography. However, the truth was more complex. In joint work with Phan Duong Hieu (of Limoges, France) we investigate the strengths and weaknesses of all sides in communications intelligence.

# The Allen-Cahn equation and a conjecture of De Giorgi

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The Allen-Cahn equation appears in the study of phase-transitions for a fluid with two-stable phases. It has been known from the work of Modica and Mortola that the level sets of the solution behave at large scales as minimal surfaces. This fact suggests that global solutions to the Allen-Cahn equation have the same rigidity properties as global minimal surfaces. In particular De Giorgi conjectured that the Bernstein theorem for minimal graphs is valid for the Allen-Cahn equation. I will discuss the history of this conjecture together with some of its nonlocal counterparts.

# Colloquium: Non-uniform Complexity in Cryptography

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Somewhat unexpectedly, a near consensus among theoreticians is that cryptographic theorems should be proved in the non-uniform model of complexity, rather than the standard uniform complexity model developed by Alan Turing, the “father of computer science.” In joint work with Alfred Menezes of the University of Waterloo, we have criticized the use of non-uniformity in cryptography, finding that even some of the most distinguished researchers have been led badly astray by their misplaced faith in non-uniformity

# Colloquium: General Relativity - Searching for Geometry of the Universe

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# Public Lecture: String Theory and the Geometry of the Universe’s Hidden Dimensions

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# String Theory and the Geometry of the Universe’s Hidden Dimensions

**Exploring the Hidden Dimensions of our Universe Through Geometry **

Shing-Tung Yau

Thursday, April 26, 2018 | 7:00pm

UCI Student Center, Crystal Cove Auditorium

*Historically, advances in mathematics and our understanding of the physical universe have often gone hand in hand. Come hear from one of the world’s most distinguished mathematicians how this close interplay has continued to deepen in recent times with new mathematical breakthroughs in geometry and exciting physical theories that propose extra hidden dimensions in our universe.*

**Shing-Tung Yau** is Harvard University’s William Caspar Graustein Chair Professor of Mathematics and Professor of Physics. His worldwide influence on mathematics and math/science education has few equals. He has made seminal contributions in many different fields of modern mathematics and also has had significant impact in physics, computer science, and technology. His many celebrated achievements include laying the mathematical foundation of Einstein’s general theory of relativity and many of today’s physical theories of spacetime with extra dimensions. Throughout his career, he has been a tireless educator having initiated a number of math and science competitions at the high school and university levels, established seven world-class mathematical research centers worldwide, and also wrote three noted popular science books. Dr. Yau was born in 1949 in Guangdong, China. He earned his Ph.D. from UC Berkeley in 1971, was appointed Professor at Stanford University in1974, and joined Harvard University in 1987. He is a member of the U.S. National Academy of Sciences, the American Academy of Arts and Sciences and the Academia Sinica. He has been awarded numerous top prizes including the Fields Medal, the MacArthur Fellowship, the Wolf Prize, and the U.S. National Medal of Science.

**Please RSVP at https://ps.uci.edu/Yau**

**Parking for this event is available for $10 at the Student Center Parking Structure located on the corner of Pereira Dr. and West Peltason. This lecture is free and open to the public. School groups and media representatives should contact Tatiana Arizaga at tarizaga@uci.edu. **