Knots and Optimal Cycles and Thoughts on AI+Mathematics+Coding

About this event

Math/CS Colloquium Series The talk will start at 3:50 p.m. in O'Connor 205. There will be cookies and pastries before the talk at 3:40 p.m. in the same classroom.All undergraduates are welcome and encouraged to attend! Cookies and pastries will be served during the talk. Details of the talk can be found below.Speaker: Anil Nirmal Hirani (University of Illinois at Urbana-Champaign)Title: Discrete Wedge Product, Associativity, and A-infinity AlgebrasAbstract: This talk shows, on screen, two problems in computational topology from about fifteen years ago, one studied with Tamal Dey and Bala Krishnamoorthy and the other with Nathan Dunfield. The first is finding the shortest cycle in a given homology class on a surface or a solid. It turns out to be solvable by linear programming, for a reason that is pleasant to explain. The second is finding the least area surface spanning a knot, the soap film the knot would hold if dipped in soap solution. Here the knot lies in a cube cut into tetrahedra, and the surface must be made of triangles of that cutting; the same linear programming idea, with more work, finds it. AI enters through the recent revival of the original code and the ease with which the old experiments could then be extended, including to knots whose soap film is not the surface of least genus. Part of the talk is a discussion with the students on using AI in mathematics and computing, and on how it may change the sociology of mathematics research. The talk is built around live computer demonstrations and assumes no background beyond curiosity.Speaker Bio: Anil Hirani is a Professor of Mathematics at the University of Illinois at Urbana-Champaign. He received his Ph.D. in Computer Science, with minors in Mathematics and in Control and Dynamical Systems, from Caltech, an M.S. in Computer Science from Stanford, and his undergraduate degree from BITS Pilani, India. He has also worked at Sun Microsystems, SONY Corporation, and NASA's Jet Propulsion Laboratory. His research is on structure-preserving discretization of exterior calculus and differential geometry, including discrete exterior calculus (DEC) and finite element exterior calculus (FEEC), and its applications in computational physics and engineering. ------------- If you hav e a disability and require a reasonable accommodation, please call Shamil Asgarli 408-554-6899, Chi-Yun Hsu 408-554-6885, or 1-800-735-2929 (TTY - California Relay).>

The talk will start at 3:50 p.m. in O'Connor 205. There will be cookies and pastries before the talk at 3:40 p.m. in the same classroom.

All undergraduates are welcome and encouraged to attend!

Cookies and pastries will be served during the talk. Details of the talk can be found below.

Speaker:

Anil Nirmal Hirani (University of Illinois at Urbana-Champaign)

Title:

Discrete Wedge Product, Associativity, and A-infinity Algebras

Abstract:

This talk shows, on screen, two problems in computational topology from about fifteen years ago, one studied with Tamal Dey and Bala Krishnamoorthy and the other with Nathan Dunfield. The first is finding the shortest cycle in a given homology class on a surface or a solid. It turns out to be solvable by linear programming, for a reason that is pleasant to explain. The second is finding the least area surface spanning a knot, the soap film the knot would hold if dipped in soap solution. Here the knot lies in a cube cut into tetrahedra, and the surface must be made of triangles of that cutting; the same linear programming idea, with more work, finds it. AI enters through the recent revival of the original code and the ease with which the old experiments could then be extended, including to knots whose soap film is not the surface of least genus. Part of the talk is a discussion with the students on using AI in mathematics and computing, and on how it may change the sociology of mathematics research. The talk is built around live computer demonstrations and assumes no background beyond curiosity.

Speaker Bio:

Anil Hirani is a Professor of Mathematics at the University of Illinois at Urbana-Champaign. He received his Ph.D. in Computer Science, with minors in Mathematics and in Control and Dynamical Systems, from Caltech, an M.S. in Computer Science from Stanford, and his undergraduate degree from BITS Pilani, India. He has also worked at Sun Microsystems, SONY Corporation, and NASA's Jet Propulsion Laboratory. His research is on structure-preserving discretization of exterior calculus and differential geometry, including discrete exterior calculus (DEC) and finite element exterior calculus (FEEC), and its applications in computational physics and engineering.

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If you have a disability and requir e a reasonable accommodation, please call Shamil Asgarli 408-554-6899, Chi-Yun Hsu 408-554-6885, or 1-800-735-2929 (TTY - California Relay).