# All Upcoming Events

On Monday at 14:15 in L4, a seminar in
the Geometry and Analysis series:

Syafiq Johar (Oxford)

Ricci Flow in Milnor Frames

*In this talk, we are going to talk about the Type I singularity on 4-dimensional manifolds foliated by homogeneous S3 evolving under the Ricci flow. We review the study on rotationally symmetric manifolds done by Angenent and Isenberg as well as by Isenberg, Knopf and Sesum. In the latter, a global frame for the tangent bundle, called the Milnor frame, was used to set up the problem. We shall look at the symmetries of the manifold, derived from Lie groups and its ansatz metrics, and this global tangent bundle frame developed by Milnor and Bianchi. Numerical simulations of the Ricci flow on these manifolds are done, following the work by Garfinkle and Isenberg, providing insight and conjectures for the main problem. Some analytic results will be proven for the manifolds S1×S3 and S4 using maximum principles from parabolic PDE theory and some sufficiency conditions for a neckpinch singularity will be provided. Finally, a problem from general relativity with similar metric symmetries but endowed on a manifold with differenttopology, the Taub-Bolt and Taub-NUT metrics, will be discussed.*

**Further information:**
On Thursday at 16:00 in L6, a seminar in
the Number Theory series:

Aled Walker (University of Cambridge)

GCD sums and sum-product estimates

*When S is a finite set of natural numbers, a GCD-sum is a particular kind of double-sum over the elements of S, and they arise naturally in several settings. In particular, these sums play a role when one studies the local statistics of point sequences on the unit circle. There are known upper bounds for the size of a GCD-sum in terms of the size of the set S, most recently due to de la Bretèche and Tenenbaum, and these bounds are sharp. Yet the known examples of sets S for which the GCD-sum over S provides a matching lower bound all possess strong multiplicative structure, whereas in applications the set S often comes with additive structure. In this talk I will describe recent joint work with Thomas Bloom in which we apply an estimate from sum-product theory to prove a much stronger upper bound on a GCD-sum over an additively structured set. I will also describe an application of this improvement to the study of the distribution of points on the unit circle, with a further application to arbitrary infinite subsets of squares.*

**Further information:**
On Monday, February 25, at 14:15 in L4, a seminar in
the Geometry and Analysis series:

Cheuk Yu Mak (Cambridge University)

TBA

On Tuesday, February 26, at 12:00 in L4, a seminar in
the Quantum Field Theory series:

Alexander Belyaev (Southampton University)

to be announced

On Tuesday, February 26, at 15:30 in L4, a seminar in
the Algebraic Geometry series:

Sven Meinhardt (Sheffield)

TBA

On Thursday, February 28, at 16:00 in L6, a seminar in
the Number Theory series:

Beth Romano (University of Cambridge)

Arithmetic statistics via graded Lie algebras

*I will talk about recent work with Jack Thorne in which we find the average size of the Selmer group for a family of genus-2 curves by analyzing a graded Lie algebra of type E_8. I will focus on the role representation theory plays in our proofs.*

**Further information:**
On Monday, March 4, at 14:15 in L4, a seminar in
the Geometry and Analysis series:

John Pardon (Princeton)

TBA

On Tuesday, March 5, at 15:30 in L4, a seminar in
the Algebraic Geometry series:

Martin Gallauer (Oxford)

TBA

On Tuesday, April 30, at 15:30 in L4, a seminar in
the Algebraic Geometry series:

Lena Gal (Oxford)

TBA

On Tuesday, May 7, at 15:30 in L4, a seminar in
the Algebraic Geometry series:

Fatemeh Mohammadi (Bristol)

TBA

On Monday, June 3, at 14:15 in L4, a seminar in
the Geometry and Analysis series:

Lukas Brantner (Oxford University)

TBA

On Tuesday, June 4, at 15:30 in L4, a seminar in
the Algebraic Geometry series:

Thomas Kahle (OvGU Madgeburg)

Linear syzygies, hyperbolic Coxeter groups and regularity

On Tuesday, October 15, at 15:30 in L4, a seminar in
the Algebraic Geometry series:

Bernd Sturmfels (Berkeley and MPI Leipzig)

TBA