Triangle Seminars
Monday, 26 Jun 2023
String compactifications, closed differential forms, and mapping cones
Li-Sheng Tseng
(UC Irvine)
Abstract:
In compactifications over smooth geometrical spaces, closed differential forms can take on a prominent role. For instance, closed forms can represent the geometrical structure of special holonomy manifolds and also fluxes that are present in the compactifications. In this talk, we will describe novel geometrical invariants that arise on manifolds with a distinguished closed form. In particular, we will show that there are natural cohomologies of mapping cone type that in general are dependent on the distinguished closed form. These cohomologies provide another tool to help count the massless scalars that arise in compactifications.
In compactifications over smooth geometrical spaces, closed differential forms can take on a prominent role. For instance, closed forms can represent the geometrical structure of special holonomy manifolds and also fluxes that are present in the compactifications. In this talk, we will describe novel geometrical invariants that arise on manifolds with a distinguished closed form. In particular, we will show that there are natural cohomologies of mapping cone type that in general are dependent on the distinguished closed form. These cohomologies provide another tool to help count the massless scalars that arise in compactifications.
Posted by: IC2
Wednesday, 28 Jun 2023
Numerical experiments on coefficients of instanton partition functions
📍 London
Aradhita Chattopadhyaya
(Dublin Institute of Advanced Studies)
Abstract:
We analyze the coefficients of partition functions of Vafa-Witten theory for the complex projective plane CP^2. We experimentally study the growth of the coefficients for gauge group SU(2) and SU(3), which are examples of mock modular forms of depth 1 and 2 respectively. We also introduce the notion of "mock cusp form'', and study an example of weight 3 related to the SU(3) partition function. Numerical experiments on the first 200 coefficients suggest that the coefficients of a mock modular form of weight k grow as the coefficients of a modular form of weight k, that is to say as n^{k-1}. On the other hand the coefficients of the mock cusp form appear to grow as n^{3/2}, which exceeds the growth of classical cusp forms of weight 3. We provide bounds using saddle point analysis, which however largely exceed the experimental observation.
We analyze the coefficients of partition functions of Vafa-Witten theory for the complex projective plane CP^2. We experimentally study the growth of the coefficients for gauge group SU(2) and SU(3), which are examples of mock modular forms of depth 1 and 2 respectively. We also introduce the notion of "mock cusp form'', and study an example of weight 3 related to the SU(3) partition function. Numerical experiments on the first 200 coefficients suggest that the coefficients of a mock modular form of weight k grow as the coefficients of a modular form of weight k, that is to say as n^{k-1}. On the other hand the coefficients of the mock cusp form appear to grow as n^{3/2}, which exceeds the growth of classical cusp forms of weight 3. We provide bounds using saddle point analysis, which however largely exceed the experimental observation.
Posted by: andrea
Thursday, 29 Jun 2023
Description:
This is a recurring meeting which brings together regional mathematical physicists at all career stages to discuss topics of recent interest in a friendly setting. It is a one day event and will be hosted at the University of Southampton on 29 June 2023.
Speakers: Aradhita Chattopadhyaya (Dublin Institute of Advanced Studies); Vaibhav Gautam (University of Surrey); Ricardo Monteiro (Queen Mary University of London); Alan Rios Fukelman (Kings College London); Arvind Shekar (University of Southampton)
More information including registration and and a link to previous (and future) events can be found in the event's website.
Early career researchers and PhD students are particularly encouraged to attend. There is funding available to cover travel expenses for PhD students and ECRs, this can be requested in the registration form.
This is a recurring meeting which brings together regional mathematical physicists at all career stages to discuss topics of recent interest in a friendly setting. It is a one day event and will be hosted at the University of Southampton on 29 June 2023.
Speakers: Aradhita Chattopadhyaya (Dublin Institute of Advanced Studies); Vaibhav Gautam (University of Surrey); Ricardo Monteiro (Queen Mary University of London); Alan Rios Fukelman (Kings College London); Arvind Shekar (University of Southampton)
More information including registration and and a link to previous (and future) events can be found in the event's website.
Early career researchers and PhD students are particularly encouraged to attend. There is funding available to cover travel expenses for PhD students and ECRs, this can be requested in the registration form.
Posted by: I.Aniceto@soton.ac.uk