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# Seminars and short courses

Seminars, for informal dissemination of research results, exploratory work by research teams, outreach activities, etc., constitute the simplest form of meetings at a Mathematics research centre.

CAMGSD has recorded the calendar of its seminars for a long time, this page serving both as a means of public announcement of forthcoming activities but also as a historic record.

For a full search interface see the Mathematics Department seminar page.

## 06/12/2021, Monday, 15:00–16:00 Europe/Lisbon — Online

Nathan Benjamin, Princeton University.

We apply the theory of harmonic analysis on the fundamental domain of $SL(2,\mathbb{Z})$ to partition functions of two-dimensional conformal field theories. We decompose the partition function of $c$ free bosons on a Narain lattice into eigenfunctions of the Laplacian of worldsheet moduli space $H/SL(2,\mathbb{Z})$, and of target space moduli space $O(c, c; \mathbb{Z})\backslash O(c, c; \mathbb{R})/O(c) × O(c)$. This decomposition manifests certain properties of Narain theories and ensemble averages thereof. We extend the application of spectral theory to partition functions of general two-dimensional conformal field theories, and explore its meaning in connection to $AdS_3$ gravity. An implication of harmonic analysis is that the local operator spectrum is fully determined by a certain subset of degeneracies.

## 07/12/2021, Tuesday, 16:30–17:30 Europe/Lisbon — Online

Ciprian Manolescu, Stanford University.

A well-known strategy to disprove the smooth 4D Poincare conjecture is to find a knot that bounds a disk in a homotopy 4-ball but not in the standard 4-ball. Freedman, Gompf, Morrison and Walker suggested that Rasmussen’s invariant from Khovanov homology could be useful for this purpose. I will describe three recent results about this strategy: that it fails for Gluck twists (joint work with Marengon, Sarkar and Willis); that an analogue works for other 4-manifolds (joint work with Marengon and Piccirillo); and that 0-surgery homeomorphisms provide a large class of potential examples (joint work with Piccirillo).

## 09/12/2021, Thursday, 17:00–18:00 Europe/Lisbon — Online

Pier Luigi Dragotti, Department of Electrical and Electronic Engineering, Imperial College, London.

The revolution in sensing, with the emergence of many new imaging techniques, offers the possibility of gaining unprecedented access tothe physical world, but this revolution can only bear fruit through the skilful interplay between the physical and computational worlds. This is the domain of computational imaging which advocates that, to develop effective imaging systems, it will be necessary to go beyond the traditional decoupled imaging pipeline where device physics, image processing and the end-user application are considered separately. Instead, we need to rethink imaging as an integrated sensing and inference model. In this talk we cover two research areas where computational imaging is likely to have an impact.

We first focus on the heritage sector which is experiencing a digital revolution driven in part by the increasing use of non-invasive, non-destructive imaging techniques. These new imaging methods provide a way to capture information about an entire painting and can give us information about features at or below the surface of the painting. We focus on Macro X-Ray Fluorescence (XRF) scanning which is a technique for the mapping of chemical elements in paintings. After describing in broad terms the working of this device, a method that can process XRF scanning data from paintings is introduced. The method is based on connecting the problem of extracting elemental maps in XRF data to Prony's method, a technique broadly used in engineering to estimate frequencies of a sum of sinusoids. The results presented show the ability of our method to detect and separate weak signals related to hidden chemical elements in the paintings. We then discuss results on the Leonardo’s The Virgin of the Rocks and show that our algorithm is able to reveal, more clearly than ever before, the hidden drawings of a previous composition that Leonardo then abandoned for the painting that we can now see.

In the second part of the talk, we focus on two-photon microscopy and neuroscience. To understand how networks of neurons process information, it is essential to monitor their activity in living tissue. Multi-photon microscopy is unparalleled in its ability to image cellular activity and neural circuits, deep in living tissue, at single-cell resolution. However, in order to achieve step changes in our understanding of brain function, large-scale imaging studies of neural populations are needed and this can be achieved only by developing computational tools that can enhance the quality of the data acquired and can scan 3-D volumes quickly. In this talk we introduce light-field microscopy and present a method to localize neurons in 3-D. The method is based on the use of proper sparsity priors, novel optimization strategies and machine learning.

This is joint work with A. Foust, P. Song, C. Howe, H. Verinaz, J. Huang and Y.Su from Imperial College London, and C. Higgitt and N. Daly from The National Gallery in London

## 13/12/2021, Monday, 15:00–16:00 Europe/Lisbon — Online

Sourav Roychowdhury, Chennai Mathematical Institute.

In this talk I will discuss Klebanov-Tseytlin background and its non-Abelian T-dual geometry. In particular I will show that the T-dual background admits pp-wave geometry in the neighbourhood of appropriate null geodesic. I will make comments on possible dual gauge theory for our pp-wave background.