Please note that the list below only shows forthcoming events, which may not include regular events that have not yet been entered for the forthcoming term. Please see the past events page for a list of all seminar series that the department has on offer.

 

Past events in this series


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. 

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, 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, 30 May 2023

10:00 - 12:00
C2

Nonlinear Fokker-Planck equations modelling large networks of neurons

Dr Pierre Roux
((Oxford University))
Further Information
Sessions led by Dr Pierre Roux will take place on

30 May 2023 10:00 - 12:00 C2

6 June 2023 15:00 - 17:00 C2

8 June 2023 10:00 - 12:00 C2

13 June 2023 15:00 - 17:00 C2

Participants should have a good knowledge of Functional Analysis; basic knowledge about PDEs and distributions; and notions in probability. Should you be interested in taking part in the course, please send an email to @email.

Abstract

PhD_course_Roux.pdf

We will start from the description of a particle system modelling a finite size network of interacting neurons described by their voltage. After a quick description of the non-rigorous and rigorous mean-field limit results, we will do a detailed analytical study of the associated Fokker-Planck equation, which will be the occasion to introduce in context powerful general methods like the reduction to a free boundary Stefan-like problem, the relative entropy methods, the study of finite time blowup and the numerical and theoretical exploration of periodic solutions for the delayed version of the model. I will then present some variants and related models, like nonlinear kinetic Fokker-Planck equations and continuous systems of Fokker-Planck equations coupled by convolution.

Tue, 30 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)_2.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, 06 Jun 2023

15:00 - 17:00
C2

Nonlinear Fokker-Planck equations modelling large networks of neurons

Dr Pierre Roux
((Oxford University) )
Further Information

Sessions led by Dr Pierre Roux will take place on

30 May 2023 10:00 - 12:00 C2

6 June 2023 15:00 - 17:00 C2

8 June 2023 10:00 - 12:00 C2

13 June 2023 15:00 - 17:00 C2

Participants should have a good knowledge of Functional Analysis; basic knowledge about PDEs and distributions; and notions in probability. Should you be interested in taking part in the course, please send an email to @email.

Abstract

PhD_course_Roux_0.pdf

We will start from the description of a particle system modelling a finite size network of interacting neurons described by their voltage. After a quick description of the non-rigorous and rigorous mean-field limit results, we will do a detailed analytical study of the associated Fokker-Planck equation, which will be the occasion to introduce in context powerful general methods like the reduction to a free boundary Stefan-like problem, the relative entropy methods, the study of finite time blowup and the numerical and theoretical exploration of periodic solutions for the delayed version of the model. I will then present some variants and related models, like nonlinear kinetic Fokker-Planck equations and continuous systems of Fokker-Planck equations coupled by convolution.

Thu, 08 Jun 2023

10:00 - 12:00
C2

Nonlinear Fokker-Planck equations modelling large networks of neurons

Dr Pierre Roux
((Oxford University))
Further Information

Sessions led by Dr Pierre Roux will take place on

30 May 2023 10:00 - 12:00 C2

6 June 2023 15:00 - 17:00 C2

8 June 2023 10:00 - 12:00 C2

13 June 2023 15:00 - 17:00 C2

Participants should have a good knowledge of Functional Analysis; basic knowledge about PDEs and distributions; and notions in probability. Should you be interested in taking part in the course, please send an email to @email.

Abstract

PhD_course_Roux_1.pdf

We will start from the description of a particle system modelling a finite size network of interacting neurons described by their voltage. After a quick description of the non-rigorous and rigorous mean-field limit results, we will do a detailed analytical study of the associated Fokker-Planck equation, which will be the occasion to introduce in context powerful general methods like the reduction to a free boundary Stefan-like problem, the relative entropy methods, the study of finite time blowup and the numerical and theoretical exploration of periodic solutions for the delayed version of the model. I will then present some variants and related models, like nonlinear kinetic Fokker-Planck equations and continuous systems of Fokker-Planck equations coupled by convolution.

Tue, 13 Jun 2023

15:00 - 17:00
C2

Nonlinear Fokker-Planck equations modelling large networks of neurons

Dr Pierre Roux
((Oxford University))
Further Information

Sessions led by Dr Pierre Roux will take place on

30 May 2023 10:00 - 12:00 C2

6 June 2023 15:00 - 17:00 C2

8 June 2023 10:00 - 12:00 C2

13 June 2023 15:00 - 17:00 C2

Participants should have a good knowledge of Functional Analysis; basic knowledge about PDEs and distributions; and notions in probability. Should you be interested in taking part in the course, please send an email to @email.

Abstract

PhD_course_Roux_2.pdf

We will start from the description of a particle system modelling a finite size network of interacting neurons described by their voltage. After a quick description of the non-rigorous and rigorous mean-field limit results, we will do a detailed analytical study of the associated Fokker-Planck equation, which will be the occasion to introduce in context powerful general methods like the reduction to a free boundary Stefan-like problem, the relative entropy methods, the study of finite time blowup and the numerical and theoretical exploration of periodic solutions for the delayed version of the model. I will then present some variants and related models, like nonlinear kinetic Fokker-Planck equations and continuous systems of Fokker-Planck equations coupled by convolution.