BICMR&TIAS Math-Physics Day August 6, 2015

Organizers and Speakers:

Zhenghan Wang (Microsoft Research and UCSB)

Xiao-Gang Wen (MIT and PI)

Zheng-Yu Weng (Tsinghua)

Weiping Zhang (Nankai)

The last few decades have been a golden age for the convergence of mathematics and physics. The application of topology and global differential geometry in condensed matter physics has been a central new theme as illustrated by topological phases of matter and topological insulators.  The idea of emergence and the phenomenon of entanglement hold the promise for a new quantum revolution in physics.  We organize this math-physics day to encourage further activities in this integration:  explaining to mathematicians by physicists what new mathematics needs to be developed, and providing further examples of the unreasonable effectiveness of mathematics in natural sciences by mathematicians.

Schedule:

August 6, Thursday

Room: Classroom 77201

Morning:

9:30am-10:30am Xiao-Gang Wen

11:00am-12:00pm Weiping Zhang

Afternoon:

2:30pm-3:30pm Zheng-Yu Weng

4:00pm-5:00pm Zhenghan Wang

Tittle and abstract:

Zhenghan Wang:

Title:  TQFTs in Nature

Abstract:  I will explain the search of topological quantum field theories (TQFTs) in real physical systems---topological phases of matter, and how higher category theory is useful for this endeavor.

Xiao-Gang Wen

Title: A theory of 2+1D topological orders in boson and fermion systems 
Abstract: I will introduce the notion of topological order and non-Abelian statistics. 
Then I will use non-Abelian statistics to obtain a simplified theory that may classify 
2+1D topological orders in boson and fermion systems. 

Zheng-yu Weng

The title: Emergent theory of high-temperature superconductivity due to strong correlations

Abstract: Conventional condensed matter physics usually deals with weakly correlated electrons. The discovery of high-temperature cuprate superconductivitors in 1986 has inspired a tremendous effort in investigating new physics emerging from strongly correlated electrons. I will discuss a novel theoretical/mathematical structure underlying a microscopic model that may be fundamental in understanding high-Tc superconductivity, and its exotic nature may call for new mathematics.

Weiping Zhang

Title: On the mod 2 index of Atiyah and Singer

Abstract: It is said that the mod 2 index introduced by Atiyah and Singer has recently played a role in the theory of topological insulators. In this talk we will survey the mathematical aspects of this delicate invariant.