Videos

CMSA/Tsinghua Math-Science Literature Lecture: Scott Sheffield (MIT): Yang-Mills theory and random surfaces

2025 Ding Shum Lecture | February 13, 2025 Speaker: Irit Dinur, Institute for Advanced Study Title: Expanders from local to global Abstract: Imagine a network—like a social network, a transportation system, or even a biological system—where every part of the network is robustly connected to the rest. Expander graphs are the mathematical idealization of such networks. They are structures where any small group of points (nodes) has many connections to the rest of the graph, ensuring that no part i...

Speaker: Bjorn Poonen, MIT Title: Ranks of elliptic curves Abstract: Elliptic curves are simplest varieties whose rational points are not fully understood, and they are the simplest projective varieties with a nontrivial group structure.  In 1922 Mordell proved that the group of rational points on an elliptic curve is finitely generated.  We will survey what is known and what is believed about this group.  

CMSA/Tsinghua Math-Science Literature Lecture 9/18/24 Speaker: Marc Lackenby, University of Oxford Title: The complexity of knots Abstract: In his final paper in 1954, Alan Turing wrote `No systematic method is yet known by which one can tell whether two knots are the same.’ Within the next 20 years, Wolfgang Haken and Geoffrey Hemion had discovered such a method. However, the computational complexity of this problem remains unknown. In my talk, I will give a survey on this area, that draws on t...

Prof. Cameron Gordon presented a lecture in the CMSA/Tsinghua Math-Science Literature Lecture Series. Title: The Unknotting Number of a Knot Abstract: One of the oldest and most natural knot invariants is the unknotting number, which is the minimum number of times a knot must be allowed to pass through itself in order to unknot it. Although this invariant was discussed by Tait almost 150 years ago, it is still poorly understood. For instance it is not known if it is algorithmically computable, a...