Events for 03/26/2025 from all calendars

Noncommutative Geometry Seminar

Time: 2:00PM - 3:00PM

Location: BLOC 302

Speaker: Xuan Yao, Cornell University

Title: On the topology of manifolds with positive intermediate curvature

Abstract: We formulate a conjecture relating the topology of a manifold's universal cover with the existence of metrics with positive $m$-intermediate curvature. We prove the result for manifolds of dimension $n\in\{3,4,5\}$ and for most choices of $m$ when $n=6$. As a corollary, we show that a closed, aspherical 6-manifold cannot admit a metric with positive $4$-intermediate curvature.

Groups and Dynamics Seminar

Time: 3:00PM - 4:00PM

Location: BLOC 628

Speaker: Yuri Bahturin, Memorial University of Newfoundland

Title: On the growth and cogrowth of subgroups in free groups and subalgebras in free Lie algebras

Abstract: The talk is based on the results of A. Yu. Olshanskii and the speaker. Important results about the growth and cogrowth of subgroups in free groups have been obtained by R. I. Grigorchuk. In this talk I will speak about the special features of the growth and cogrowth when the subgroups are subnormal and the subalgebras are subideals. One says that a subgroup H of a group G is subnormal if there is a descending chain of subgroups G=H_0>H_1>...>H_k=H with every term being a normal subgroup in the previous one. Similarly one defines subideals in an algebra. Thus the growth and cogrowth then give a picture intermediate between these values, say, for normal subgroups and general finitely generated subgroups.

Noncommutative Geometry Seminar

Time: 4:00PM - 5:00PM

Location: BLOC 628

Speaker: Thorsten Hertl, University of Melbourne

Title: Moduli Spaces of Positive Curvature Metrics

Abstract: In the last decade the observer moduli space of Riemannian metrics with positive curvature conditions have become more and more popular. So far, results in this direction only work if the dimension of the underlying manifold is bigger than 5 or if the manifold is spin. I will present a different construction that works in dimension 4 and does not rely on spin geometry.