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. 

We study the inverse problem of determining both the source of a wave and its speed inside a medium from measurements of the solution of the wave equation on the boundary. This problem arises in photoacoustic and thermoacoustic tomography, and has important applications in medical imaging. We prove that if $c^{-2}$ is harmonic in $\omega \subset \R^3$ and identically 1 on $\omega^c$, where $\omega$ is a simply connected region, then a non-trapping wave speed $c$ can be uniquely determined from the solution of the wave equation on boundary of $\Omega \supset \supset \omega$ without the knowledge of the source. We also show that if the wave speed $c$ is known and only assumed to be bounded then, under mild assumptions on the set of discontinuous points of $c$, the source of the wave can be uniquely determined from boundary measurements.

In  Ramsey  Theory, ultrafilters often play an instrumental role.
By using nonstandard models of the integers, one can replace those
third-order objects (ultrafilters are families of subsets) by simple
points.

In this talk we present a nonstandard technique that is grounded
on the above observation, and show its use in proving some new results
in Ramsey Theory of Diophantine equations.
 

A classical result of Goldman states that character variety of an oriented surface is a symplectic algebraic variety, and that the Goldman Lie algebra of free loops on the surface acts by Hamiltonian vector fields on the character variety. I will describe a vast generalization of these results, including to higher dimensional manifolds where the role of the Goldman Lie algebra is played by the Chas-Sullivan string bracket in the string topology of the manifold. These results follow from a general statement in noncommutative geometry. In addition to generalizing Goldman's result to string topology, we obtain a number of other interesting consequences including the universal Hitchin system on a Riemann surface. This is joint work with Chris Brav.