Seminars in Mathematical Sciences

Seminars in the next week
Sep 28 (Thu)

14:00 MCS2068 ProbClément Cosco (Paris Dauphine): Directed polymers in random environment and the critical dimension

The model of directed polymers describe the behavior of a long, directed chain that spreads among an inhomogeneous environment which may attract or repulse the polymer. When the spacial dimension is larger than three, a phase transition occurs between diffusivity (high temperature) and localization (low temperature). On the other hand, in dimensions one and two the polymer is always localized. Dimension two is however critical, as one can recover a phase transition by letting the temperature tend to infinity under a specific parametrization (Caravenna-Sun-Zygouras 17’). In this talk, I will present some of the main results that are known about this scaling regime, and discuss the recent advances that have occurred in the past few years. In particular, I will describe some results that I have obtained with my coauthors (Anna Donadini, Shuta Nakajima and Ofer Zeitouni) on the diffusive phase and its relation to Gaussian logarithmically correlated fields.

Venue: MCS2068

15:30 MCS2068 ProbRongfeng Sun (NU Singapore): Some properties of the critical 2d stochastic heat flow

The critical 2d stochastic heat flow (SHF) was previously constructed via the scaling limit of directed polymer partition functions in the critical dimension d=2 and in the critical window. It can be interpreted as the solution of the critical 2d stochastic heat equation with multiplicative space-time white noise. In this talk, we will discuss more recent results on the properties of the critical 2d SHF, including the fact that it cannot be a Gaussian multiplicative chaos, and it is almost surely singular with respect to the Lebesgue measure. Based on joint work with F. Caravenna and N. Zygouras.

Venue: MCS2068

Oct 03 (Tue)

15:00 MCS3070 APDEGeorgios Domazakis (Durham University): The rigidity of equality cases for perimeter inequality under Schwarz symmetrisation

This talk will discuss the rigidity of equality cases for perimeter inequality under Schwarz symmetrisation. The term rigidity refers to the situation in which the equality cases are only obtained by translations of the Schwarz symmetric set. First, we will discuss the existing results in literature related to the corresponding rigidity problem. Then, we will present sufficient and necessary conditions for rigidity under this framework. Our analysis will be based on the properties of the corresponding distribution function and on a careful study of the transformations that can be applied to the symmetric set, without creating any perimeter contribution.

Venue: MCS3070

Oct 05 (Thu)

13:00 MCS3070 G&TMasoumeh Zarei (Münster): TBA

Venue: MCS3070


Click on title to see abstract. Zoom links, if available, are given for today's seminars only.

Upcoming Seminars by Series
(Click on series to expand.)
• Amplitudes and Correlators

Contact: arthur.lipstein@durham.ac.uk

No upcoming seminars have been scheduled (not unusual outside term time or during industrial actions).

• Analysis and PDE

Usual Venue: MCS2068

Contact: alpar.r.meszaros@durham.ac.uk

Oct 03 15:00 Georgios Domazakis (Durham University): The rigidity of equality cases for perimeter inequality under Schwarz symmetrisation

This talk will discuss the rigidity of equality cases for perimeter inequality under Schwarz symmetrisation. The term rigidity refers to the situation in which the equality cases are only obtained by translations of the Schwarz symmetric set. First, we will discuss the existing results in literature related to the corresponding rigidity problem. Then, we will present sufficient and necessary conditions for rigidity under this framework. Our analysis will be based on the properties of the corresponding distribution function and on a careful study of the transformations that can be applied to the symmetric set, without creating any perimeter contribution.

Venue: MCS3070

Dec 05 15:00 Dave Smith (Yale/NUS Singapore): Fokas Diagonalization

We describe a new form of diagonalization for linear two point constant coefficient differential operators with arbitrary linear boundary conditions. Although the diagonalization is in a weaker sense than that usually employed to solve initial boundary value problems (IBVP), we show that it is sufficient to solve IBVP whose spatial parts are described by such operators. We argue that the method described may be viewed as a reimplementation of the Fokas transform method for linear evolution equations on the finite interval. The results are extended to multipoint and interface operators, including operators defined on networks of finite intervals, in which the coefficients of the differential operator may vary between subintervals, and arbitrary interface and boundary conditions may be imposed; differential operators with piecewise constant coefficients are thus included.

Venue: MCS3070

Jan 23 15:00 Matteo Capoferri (Heriot-Watt University): TBA

TBA

Venue: MCS3070

• Applied Mathematics

Usual Venue: MCS2052

Contact: andrew.krause@durham.ac.uk

No upcoming seminars have been scheduled (not unusual outside term time or during industrial actions).

• Arithmetic Study Group

Usual Venue: MCS2068

Contact: alexander.mangerel@durham.ac.uk

No upcoming seminars have been scheduled (not unusual outside term time or during industrial actions).

• CPT Colloquium

Usual Venue: OC218

Contact: p.e.dorey@durham.ac.uk

For more information, see HERE.


No upcoming seminars have been scheduled (not unusual outside term time or during industrial actions).

• Department Research Colloquium

Usual Venue: MCS0001

Contact: inaki.garcia-etxebarria@durham.ac.uk,sunil.chhita@durham.ac.uk

No upcoming seminars have been scheduled (not unusual outside term time or during industrial actions).

• Distinguished and Public Lectures

Usual Venue: MCS0001

Contact: p.e.dorey@durham.ac.uk

No upcoming seminars have been scheduled (not unusual outside term time or during industrial actions).

• Ergodic Theory and Dynamics

Usual Venue: MCS3070

Contact: gabriel.fuhrmann@durham.ac.uk

No upcoming seminars have been scheduled (not unusual outside term time or during industrial actions).

• Geometry and Topology

Usual Venue: MCS2068

Contact: martin.p.kerin@durham.ac.uk

Recordings of past seminars can be found HERE.


Oct 05 13:00 Masoumeh Zarei (Münster): TBA

Venue: MCS3070

Oct 12 13:00 Clemens Saemann (Oxford): TBA

Venue: MCS2068

Oct 19 13:00 Artemis Vogiatzi (Queen Mary University of London):

Venue: MCS3070

Nov 02 13:00 Anthea Monod (Imperial): TBA

Venue: MCS2068

Nov 09 13:00 Pascal Stiefenhofer (Newcastle): TBA

Venue: MCS2068

Nov 16 13:00 Nivedita Viswanathan (Brunel University London):

Venue: MCS3070

Nov 23 13:00 Claudius Zibrowius (Durham): TBA

Venue: MCS3070

Nov 30 13:00 Jaime Santos-Rodríguez (Durham/UAM): TBA

Venue: MCS3070

Dec 07 13:00 Marie-Amélie Lawn (Imperial): TBA

Venue: MCS2068

Jan 11 13:00 Brendan Guilfoyle (Munster Technological University): TBA

Venue: MCS2068

Jan 18 13:00 Andrey Lazarev (Lancaster): TBA

Venue: MCS2068

Feb 22 13:00 Lawrence Mouillé (Syracuse University): TBA

Venue: MCS2068

May 16 13:00 Asma Hassannezhad (Bristol): TBA

Venue: MCS3070

• HEP Journal Club

Usual Venue: MCS3070

Contact: andrea.grigoletto@durham.ac.uk,nakarin.lohitsiri@durham.ac.uk

No upcoming seminars have been scheduled (not unusual outside term time or during industrial actions).

• HEP Lunchtime

Usual Venue: MCS0001

Contact: silvia.nagy@durham.ac.uk,ana.retore@durham.ac.uk

The talks will be held in person in MCS2068 and streamed on zoom for those who cannot attend (see abstract for link).


No upcoming seminars have been scheduled (not unusual outside term time or during industrial actions).

• Probability

Usual Venue: MCS2068

Contact: kohei.suzuki@durham.ac.uk

Sep 28 14:00 Clément Cosco (Paris Dauphine): Directed polymers in random environment and the critical dimension

The model of directed polymers describe the behavior of a long, directed chain that spreads among an inhomogeneous environment which may attract or repulse the polymer. When the spacial dimension is larger than three, a phase transition occurs between diffusivity (high temperature) and localization (low temperature). On the other hand, in dimensions one and two the polymer is always localized. Dimension two is however critical, as one can recover a phase transition by letting the temperature tend to infinity under a specific parametrization (Caravenna-Sun-Zygouras 17’). In this talk, I will present some of the main results that are known about this scaling regime, and discuss the recent advances that have occurred in the past few years. In particular, I will describe some results that I have obtained with my coauthors (Anna Donadini, Shuta Nakajima and Ofer Zeitouni) on the diffusive phase and its relation to Gaussian logarithmically correlated fields.

Venue: MCS2068

Sep 28 15:30 Rongfeng Sun (NU Singapore): Some properties of the critical 2d stochastic heat flow

The critical 2d stochastic heat flow (SHF) was previously constructed via the scaling limit of directed polymer partition functions in the critical dimension d=2 and in the critical window. It can be interpreted as the solution of the critical 2d stochastic heat equation with multiplicative space-time white noise. In this talk, we will discuss more recent results on the properties of the critical 2d SHF, including the fact that it cannot be a Gaussian multiplicative chaos, and it is almost surely singular with respect to the Lebesgue measure. Based on joint work with F. Caravenna and N. Zygouras.

Venue: MCS2068

• Pure Maths Colloquium

Usual Venue: MCS0001

Contact: raphael.zentner@durham.ac.uk

No upcoming seminars have been scheduled (not unusual outside term time or during industrial actions).

• Spectra and Moduli

Usual Venue: MCS3070

Contact: irving.d.calderon-camacho@durham.ac.uk,joe.thomas@durham.ac.uk

No upcoming seminars have been scheduled (not unusual outside term time or during industrial actions).

• Statistics

Usual Venue: MCS2068

Contact: hyeyoung.maeng@durham.ac.uk,andrew.iskauskas@durham.ac.uk

No upcoming seminars have been scheduled (not unusual outside term time or during industrial actions).