Seminars in Mathematical Sciences

Seminars in the next week
Apr 09 (Thu)

13:00 MCS3070 ApplRobert Van Gorder (Otago): Geometrically confined quantum systems

You will likely be familiar with the notion of a hydrogen atom, having seen something about its discrete energy levels and orbitals at some point or another. This is an example of a quantum system. In this talk, we explore what transpires when taking a quantum system and placing it into a three-dimensional container having some prescribed geometry. In the limit where the container is large (relative to the natural lengthscale of the quantum system), its influence over the quantum system is negligible; yet, as the container is made small (comparable to the aforementioned lengthscale), geometric information intrinsic to the container plays an important role in determining the energy and orbital structure of the system. We describe how to do (numerically-assisted) perturbation theory in this small-container limit and then match it to the large-box regime, using a combination of these asymptotics and direct simulations to tell the story of geometrically confined quantum systems. Much of our focus will be on linear Schrödinger equations governing single-particle quantum systems; however, time permitting, we will briefly discuss how to do similar things to study geometrically confined nonlinear Schrödinger equations, with geometric confinement of Bose-Einstein condensates being a primary motivation. Geometric confinement of an attractive Bose-Einstein condensate can, for instance, modify the collapse threshold and enhance stability, with the particular choice of confining geometry shifting the boundary of instability, staving off the collapse which is prevalent in three-dimensional attractive condensates.

Venue: MCS3070


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Upcoming Seminars by Series

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• Amplitudes and Correlators

Contact: arthur.lipstein@durham.ac.uk

No upcoming seminars have been scheduled (not unusual outside term time).

• Analysis and PDE

Usual Venue: MCS2068

Contact: yohance.a.osborne@durham.ac.uk

No upcoming seminars have been scheduled (not unusual outside term time).

• Applied Mathematics

Usual Venue: MCS3070

Contact: andrew.krause@durham.ac.uk

Apr 09 13:00 Robert Van Gorder (Otago): Geometrically confined quantum systems

You will likely be familiar with the notion of a hydrogen atom, having seen something about its discrete energy levels and orbitals at some point or another. This is an example of a quantum system. In this talk, we explore what transpires when taking a quantum system and placing it into a three-dimensional container having some prescribed geometry. In the limit where the container is large (relative to the natural lengthscale of the quantum system), its influence over the quantum system is negligible; yet, as the container is made small (comparable to the aforementioned lengthscale), geometric information intrinsic to the container plays an important role in determining the energy and orbital structure of the system. We describe how to do (numerically-assisted) perturbation theory in this small-container limit and then match it to the large-box regime, using a combination of these asymptotics and direct simulations to tell the story of geometrically confined quantum systems. Much of our focus will be on linear Schrödinger equations governing single-particle quantum systems; however, time permitting, we will briefly discuss how to do similar things to study geometrically confined nonlinear Schrödinger equations, with geometric confinement of Bose-Einstein condensates being a primary motivation. Geometric confinement of an attractive Bose-Einstein condensate can, for instance, modify the collapse threshold and enhance stability, with the particular choice of confining geometry shifting the boundary of instability, staving off the collapse which is prevalent in three-dimensional attractive condensates.

Venue: MCS3070

• Arithmetic Study Group

Usual Venue: MCS2068

Contact: herbert.gangl@durham.ac.uk

No upcoming seminars have been scheduled (not unusual outside term time).

• CPT Colloquium

Usual Venue: OC218

Contact: mohamed.anber@durham.ac.uk

For more information, see HERE.


No upcoming seminars have been scheduled (not unusual outside term time).

• 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).

• Distinguished and Public Lectures

Usual Venue: MCS0001

Contact: sabine.boegli@durham.ac.uk,alpar.r.meszaros@durham.ac.uk

No upcoming seminars have been scheduled (not unusual outside term time).

• Education and Pedagogy

Usual Venue: MCS3052

Contact: andrew.krause@durham.ac.uk

No upcoming seminars have been scheduled (not unusual outside term time).

• Gandalf

Usual Venue: MCS3070

Contact: daniel.n.disney@durham.ac.uk

No upcoming seminars have been scheduled (not unusual outside term time).

• Geometry and Topology

Usual Venue: MCS2068

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

Apr 30 13:00 Anthea Monod (Imperial): TBA

Venue: MCS2068

May 07 13:00 Wilhelm Klingenberg (Durham): TBA

Venue: MCS2068

May 14 13:00 Victoria Pelayo Alvaredo (Universidad Autónoma de Madrid/ICMAT): TBA

Venue: MCS2068

• HEP Journal Club

Usual Venue: MCS3070

Contact: mendel.t.nguyen@durham.ac.uk

No upcoming seminars have been scheduled (not unusual outside term time).

• HEP Lunchtime

Usual Venue: MCS0001

Contact: p.e.dorey@durham.ac.uk,enrico.andriolo@durham.ac.uk,tobias.p.hansen@durham.ac.uk

No upcoming seminars have been scheduled (not unusual outside term time).

• Probability

Usual Venue: MCS2068

Contact: tyler.helmuth@durham.ac.uk,oliver.kelsey-tough@durham.ac.uk

No upcoming seminars have been scheduled (not unusual outside term time).

• Pure Maths Colloquium

Usual Venue: MCS2068

Contact: michael.r.magee@durham.ac.uk

Apr 28 15:00 Sergey Fomin (U Michigan): Incidence geometry and tiled surfaces

We show that various classical theorems of linear incidence geometry, such as the theorems of Pappus, Desargues, Möbius, and so on, can be interpreted as special cases of a general result that involves a tiling of a closed oriented surface by quadrilateral tiles. This yields a general mechanism for producing new incidence theorems and generalizing and interpreting the known ones.

This is joint work<https://arxiv.org/abs/2305.07728> with Pavlo Pylyavskyy<https://cse.umn.edu/math/pavlo-pylyavskyy>.

Venue: MCS0001

• Spectra and Moduli

Usual Venue: MCS3070

Contact: joe.thomas@durham.ac.uk

No upcoming seminars have been scheduled (not unusual outside term time).

• 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).

• Stats4Grads

Contact: adam.stone2@durham.ac.uk

No upcoming seminars have been scheduled (not unusual outside term time).

Special Series

These link to some of the special events hosted by the Department:


• [LMS|EPSRC] Durham Symposia (from 1974)
• Collingwood Lectures (from 1984)