Tue, 23 May 2023
15:30
C4

Multivalued Dir-Minimizing Functions

Dr Immanuel Ben Porat
((Oxford University))
Further Information

The course will serve as an introduction to the theory of multivalued Dir-minimizing functions, which can be viewed as harmonic functions which attain multiple values at each point.

Aimed at Postgraduate students interested in geometric measure theory and its link with elliptic PDEs, a solid knowledge of functional analysis and Sobolev spaces, acquaintance with variational
methods in PDEs and some basic geometric measure theory are recommended.

Sessions led by Dr Immanuel Ben Porat will take place on

09 May 2023 15:30 - 17:30 C4

16 May 2023 15:30 - 17:30 C4

23 May 2023 15:30 - 17:30 C4

30 May 2023 15:30 - 17:30 C4

Should you be interested in taking part in the course, please send an email to @email.

Abstract

COURSE_PROPOSAL (12)_1.pdf

The space of unordered tuples. The notion of differentiability and the theory of metric Sobolev in the context of multi-valued functions. Multivalued maximum principle and Holder regularity. Estimates on the Hausdorff dimension of the singular set of Dir-minimizing functions. If time permits: mass minimizing currents and their link with Dir-minimizers. 

Tue, 16 May 2023
15:30
C4

Multivalued Dir-Minimizing Functions

Dr Immanuel Ben Porat
((Oxford University))
Further Information

The course will serve as an introduction to the theory of multivalued Dir-minimizing functions, which can be viewed as harmonic functions which attain multiple values at each point.

Aimed at Postgraduate students interested in geometric measure theory and its link with elliptic PDEs, a solid knowledge of functional analysis and Sobolev spaces, acquaintance with variational
methods in PDEs and some basic geometric measure theory are recommended.

Sessions led by  Dr Immanuel Ben Porat will take place on

09 May 2023 15:30 - 17:30 C4

16 May 2023 15:30 - 17:30 C4

23 May 2023 15:30 - 17:30 C4

30 May 2023 15:30 - 17:30 C4

Should you be interested in taking part in the course, please send an email to @email.

Abstract

COURSE_PROPOSAL (12)_0.pdf

The space of unordered tuples. The notion of differentiability and the theory of metric Sobolev in the context of multi-valued functions. Multivalued maximum principle and Holder regularity. Estimates on the Hausdorff dimension of the singular set of Dir-minimizing functions. If time permits: mass minimizing currents and their link with Dir-minimizers. 

Tue, 09 May 2023
15:30
C4

Multivalued Dir-Minimizing Functions

Dr Immanuel Ben Porat
(University of Oxford)
Further Information

The course will serve as an introduction to the theory of multivalued Dir-minimizing functions, which can be viewed as harmonic functions which attain multiple values at each point.

Aimed at Postgraduate students interested in geometric measure theory and its link with elliptic PDEs, a solid knowledge of functional analysis and Sobolev spaces, acquaintance with variational
methods in PDEs, and some basic geometric measure theory are recommended.

Sessions led by  Dr Immanuel Ben Porat will take place on

09 May 2023 15:30 - 17:30 C4

16 May 2023 15:30 - 17:30 C4

23 May 2023 15:30 - 17:30 C4

30 May 2023 15:30 - 17:30 C4

Should you be interested in taking part in the course, please send an email to @email.

Abstract

COURSE_PROPOSAL (12).pdf

The space of unordered tuples. The notion of differentiability and the theory of metric Sobolev in the context of multi-valued functions. Multivalued maximum principle and Holder regularity. Estimates on the Hausdorff dimension of the singular set of Dir-minimizing functions. If time permits: mass minimizing currents and their link with Dir-minimizers. 

Fri, 03 Mar 2023
16:00
C4

Integrability I

Adam Kmec
Further Information

Junior Strings is a seminar series where DPhil students present topics of common interest that do not necessarily overlap with their own research area. This is primarily aimed at PhD students and post-docs but everyone is welcome.

Fri, 11 Nov 2022
16:00
C4

The Dark Dimension

Joseph McGovern
Further Information

Junior Strings is a seminar series where DPhil students present topics of common interest that do not necessarily overlap with their own research area. This is primarily aimed at PhD students and post-docs but everyone is welcome.

Fri, 04 Nov 2022

12:00 - 13:00
C4

Short Talks from Algebra PhD Students

Algebra DPhil Students
Further Information

A collection of bite-size 10-15 minute talks from current DPhil students in the Algebra group. The talks will be accessible to masters students and above.

With plenty of opportunity to chat to current students about what doing a PhD in algebra and representation theory is like!

Wed, 09 Mar 2022

16:00 - 17:00
C4

Knot projections in 3-manifolds other than the 3-sphere

Adele Jackson
(University of Oxford)
Abstract

Knot projections for knots in the 3-sphere allow us to easily describe knots, compute invariants, enumerate all knots, manipulate them under Reidemister moves and feed them into a computer. One might hope for a similar representation of knots in general 3-manifolds. We will survey properties of knots in general 3-manifolds and discuss a proposed diagram-esque representation of them.

Mon, 28 Feb 2022

16:00 - 17:00
C4

Joint moments of characteristic polynomials of random unitary matrices

Arun Soor
Abstract

The moments of Hardy’s function have been of interest to number theorists since the early 20th century, and to random matrix theorists especially since the seminal work of Keating and Snaith, who were able to conjecture the leading order behaviour of all moments. Studying joint moments offers a unified approach to both moments and derivative moments. In his 2006 thesis, Hughes made a version of the Keating-Snaith conjecture for joint moments of Hardy’s function. Since then, people have been calculating the joint moments on the random matrix side. I will outline some recent progress in these calculations. This is joint work with Theo Assiotis, Benjamin Bedert, and Mustafa Alper Gunes.

Mon, 14 Feb 2022

16:00 - 17:00
C4

TBA

Mon, 17 Jan 2022

16:00 - 17:00
C4

Classical Mechanics and Diophantine Equations

Jay Swar
Abstract

We'll sketch how the $K$-rational solutions of a system $X$ of multivariate polynomials can be viewed as the solutions of a "classical mechanics" problem on an associated affine space.

When $X$ has a suitable topology, e.g. if its $\mathbb{C}$-solutions form a Riemann surface of genus $>1$, we'll observe some of the advantages of this new point of view such as a relatively computable algorithm for effective finiteness (with some stipulations). This is joint work with Minhyong Kim.
 

Subscribe to C4