BICMR & IAS Math-Physics Day


Zhenghan Wang (Microsoft Research and UCSB)

Xiao-Gang Wen (MIT and PI)

Zheng-Yu Weng (Tsinghua)

Weiping Zhang (Nankai)    

Date 2015-08-06 

Venue Classroom 77201

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.


August 6, Thursday

Room: Classroom 77201


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

11:00am-12:00pm Weiping Zhang


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

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.