Title: Symplectic geometry and inscription problems Speaker: Josh Greene (Boston College) Date, Time, Location: Wednesday, December 4th @4:30PM in Math Hall 520 Abstract: The square peg problem was posed by Otto Toeplitz in 1911. It asks whether every Jordan curve in the plane contains the vertices of a square, and it is still open to […]
Title: Some new perspectives in the Langlands program Speaker: Professor Matthew Emerton (University of Chicago) Date, Time, Location: Wednesday, November 20th @4:30PM in Math Hall 520 Abstract: The goal of this talk is to explain some recent (so-called “categorical”) perspectives on the Langlands program. I will gently lead up to these new developments, beginning with […]
Title: Exploring Stability in Geometric and Functional Inequalities Speaker: Alessio Figalli (ETH) Date, Time, Location: Wednesday, November 13th @4:30PM in Math Hall 520 Abstract: In the realms of analysis and geometry, geometric and functional inequalities are of paramount significance, influencing a variety of problems. Traditionally, the focus has been on determining precise constants and identifying minimizers. […]
Title: The stability-compactness method and qualitative properties of nonlinear elliptic PDEs Speaker: Henri Berestycki (University of Maryland, College Park & EHESS, Paris) Date, Time, Location: Wed. October 16th @ 4:30 PM in 520 Math Hall Abstract: Nonlinear elliptic equations describe the stationary states of numerous systems in physics, biology and medicine. Qualitative properties such as monotonicity, […]
Title: Matrix Rigidity Speaker: Josh Alman (Columbia CS) Date, Time, Location: Wed. Sept 25 @ 4:30 PM in 520 Math Hall Abstract: A matrix is called rigid if one must change many of its entries before it becomes a low-rank matrix. Leslie Valiant introduced the notion in 1977 as a tool to prove lower bounds […]
Title: Matrix Rigidity Abstract: A matrix is called rigid if one must change many of its entries before it becomes a low-rank matrix. Leslie Valiant introduced the notion in 1977 as a tool to prove lower bounds on the number of arithmetic operations needed to compute linear transformations like the discrete Fourier transform. Since then, […]
Title: Symmetries of manifolds Abstract: Whenever one studies a mathematical object one ought also to study its symmetries. Manifolds are the central objects of study in topology and geometry, and their groups of symmetries come in many flavours (isometries, diffeomorphisms, homeomorphisms, …). I will discuss some classical and recent results about the spaces of all symmetries […]
Special time, location: Tue. Feb. 27, 4:10-5:25pm, 407 Math Title: Universally counting curves in Calabi–Yau threefolds Abstract: Statements such as “there is a unique line between any pair of distinct points in the plane” and “there are 27 lines on any cubic surface” have given rise to the modern theory of enumerative geometry. To define […]
Title: Curvature blow up at big bang singularities Abstract: Singularities have been accepted as a natural feature in general relativity since the appearance of the singularity theorems of Hawking and Penrose. But these theorems do not say much concerning the nature of singularities. Do the gravitational fields become unbounded? Can the spacetime be extended through […]
Title: On High Girth Steiner-Triple Systems and Subspace Designs Abstract: We discuss the recent resolutions of the 1973 conjecture of Erdős on the existence of high girth Steiner triple systems and the existence of subspace designs. The talk will focus on placing these results within the context of classical design theory and within recent advances in the […]