Date/Time : 27 Oct 2021 16:00
Venue : via Zoom
Speaker : Beatrice Pozzetti, University of Heidelberg

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https://nus-sg.zoom.us/j/87511476637?pwd=VURaUDVzaHpMYmduN2Fod0h0Y29sQT09

Meeting ID: 875 1147 6637
Passcode: 468399

Abstract:  Surprisingly there exist connected components of character varieties of fundamental groups of surfaces in semisimple Lie groups only consisting of injective representations with discrete image. Guichard and Wienhard introduced the notion of $\Theta$ positive representations as a conjectural framework to explain this phenomena. I will discuss joint work with Jonas Beyrer in which we establish several geometric properties of $\Theta$ positive representations in PO(p,q). As an application we deduce that they indeed form connected components of character varieties.

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Date/Time : 27 Oct 2021 15:00
Venue : via Zoom
Speaker : Tomasz Przezdziecki, University of Edinburgh

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https://nus-sg.zoom.us/j/81363430790?pwd=ODk2Qko1aGhPVW9LS0Y0aDJrTG9uZz09

Meeting ID: 813 6343 0790
Passcode: 720832

Abstract: We consider a family of KLR-type algebras associated to the infinite linear quiver with an involution and a framing. We approach their representation theory through categorification and combinatorics. Orientifold KLR algebras are known to categorify highest weight modules over the Enomoto-Kashiwara algebra and their canonical bases. Using a new shuffle realization of these modules, together with a combinatorial construction of their PBW and canonical bases in terms of Lyndon words, we are able to classify irreducibles and prove finite global dimension.

The second part of the talk is devoted to the connection between orientifold KLR algebras and quantum Kac-Moody symmetric pairs. The key role is played by a Schur-Weyl duality type functor, generalizing a construction due to Kang, Kashiwara and Kim. We explain the connection between the framing in the definition of the orientifold KLR algebra, parameters of a coideal subalgebra, and the poles of meromorphic K-matrices. We present some properties of this functor and formulate a conjecture that, under appropriate assumptions, it induces an equivalence of categories.

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Date/Time : 27 Oct 2021 17:00
Venue : via Zoom
Speaker : Mars Yamaleev, Kazan Federal University

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https://nus-sg.zoom.us/j/83049258042?pwd=UWViaWNvTFUrdFdhOHJCdEVydnVkdz09

Meeting ID: 83049258042
Passcode: 1729=x3+y3

Abstract: In our talk we consider relative enumerability of 2-c.e. Turing degrees in c.e. degrees below them. We focus on an old question which arises from the well-known work of Soare and Stob in 1982. The Soare-Stob theorem says that for any noncomputable low c.e. Turing degree a there exists a non-c.e. Turing degree d which is above a and relative enumerable in a. The question is whether the degree d can always be chosen as 2-c.e. We answer this question by showing that for some the degree d must be beyond 2-c.e., and discuss the ideas of proof.  Also we consider possible generalizations of this result.

All results are obtained in a joint work with Arslanov M.M. and Batyrshin I.I.

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Date/Time : 22 Oct 2021 10:00
Venue : via Zoom
Speaker : Lee Hwee Kuan, Bioinformatics Institute, Agency for Science, Technology and Research

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https://nus-sg.zoom.us/j/9775606531?pwd=cVZ6eTRYS3ZzVUlFNXRuSlhMVjJSUT09

Meeting ID: 977 560 6531
Passcode: 123321

Abstract:  A novel weakly supervised tasks has been developed inspired by an application on cancer diagnosis. Given a bag of instances, we ask the question of how many unique classes of objects there are in the bag. This task was presented for the first time in our recent paper. Developing this task was inspired by the need to ask this question. “Given a cancer tissue sample, how many type of cancer cells there are in this sample”. We call this unique class count and formally proved that unique class count problem can be solved using a deep neural network in the multiple instance learning paradigm. We further apply our algorithm to prediction tumour purity in a cancer tissue sample. Tumour purity is the proportion of cancer cells in the tumour tissue. An accurate tumour purity estimation is crucial for accurate pathologic evaluation and for sample selection to minimize normal cell contamination in high throughput genomic analysis. Moreover, spatial tumour purity maps can help better understand the tumour microenvironment as a key determinant in tumour formation and therapeutic response.

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Date/Time : 20 Oct 2021 09:00
Venue : via Zoom
Speaker : Siqi He, Stony Brook University

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https://nus-sg.zoom.us/j/88336974987?pwd=SVVRVStaVTJ6STVEL1JGRSsxQjVFdz09

Meeting number：883 3697 4987
Password：132347

Abstract: Special Lagrangian submanifolds are a distinguished class of real calibrated submanifolds defined in a Calabi-Yau manifold, which are calibrated by the real part of the holomorphic volume form. Given a compact, smooth special Lagrangian submanifold, Mclean proved that the space of nearby special Lagrangian submanifolds of it could be parametrized by the harmonic 1-forms. In this talk, we will discuss some recent progress on generalizing Mclean’s result to the branched deformations. We will describe how to use multi-valued harmonic functions to construct branched nearby deformations.

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Date/Time : 20 Oct 2021 16:00
Venue : via Zoom
Speaker : Yang Yue, National University of Singapore

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https://nus-sg.zoom.us/j/83049258042?pwd=UWViaWNvTFUrdFdhOHJCdEVydnVkdz09

Meeting ID: 830 4925 8042
Passcode: 1729=x3+y3

Abstract:  This is a follow up of Liao Yuke’s talk last week. I will explain in detail his result which says that there exists a recursive coloring f: N -> {0,1} such that for all infinite subset X of N, if FS(X) is homogeneous for f, then X is not recursive in 0”. Here FS(X) is the set of all finite sums of distinct elements of X. Liao Yuke’s result improved Blass, Hirst and Simpson’s theorem in 1987 (from no 0′
recursive solutions to no 0” recursive ones).

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Date/Time : 20 Oct 2021 14:00
Venue : via Zoom
Speaker : Wen-Wei Li, Peking University

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https://nus-sg.zoom.us/j/81065287062?pwd=ajhROWc5MWV1RVQzQ1ZkS2NNcHp1Zz09

Meeting ID: 810 6528 7062
Passcode: 121544

Abstract:  A theory of endoscopy for the metaplectic covering Mp(2n) of Sp(2n) was proposed by the author ten years ago, and the elliptic part of the Arthur-Selberg trace formula has been stabilized since then. In this talk, I will give an overview of the stabilization of the full trace formula (arXiv:2109.06581) for these coverings, which is indispensable for global applications. This is largely inspired by the prior works of Arthur and Moeglin-Waldspurger for linear reductive groups.

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Date/Time : 18 Oct 2021 10:00
Venue : via Zoom
Speaker : Zhennan Zhou, Peking University

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https://nus-sg.zoom.us/j/85127734314?pwd=amUyZjZEdTQycEhETWNESlFDMEdoUT09

Meeting ID: 851 2773 4314
Passcode: 348196

Abstract:  In this talk, we are concerned with the Fokker-Planck equations associated with the Nonlinear Noisy Leaky Integrate-and-Fire model for neuron networks. Due to the jump mechanism at the microscopic level, such Fokker-Planck equations are endowed with an unconventional structure: transporting the boundary flux to a specific interior point. In the first part of the talk, we present a conservative and positivity preserving scheme for these Fokker-Planck equations, and we show that in the linear case, the semi-discrete scheme satisfies the discrete relative entropy estimate, which essentially matches the only known long time asymptotic solution property. We also provide extensive numerical tests to verify the scheme properties, and carry out several sets of numerical experiments, including finite-time blowup, convergence to equilibrium and capturing time-period solutions of the variant models. Secondly, we are concerned with a kinetic model for neuron networks. Individual neurons are characterized by their voltage and conductance, the dynamics of the voltage is influenced by the conductance and when the voltage is reaching a threshold, it is immediately reset to a lower value. By exploring a series of toy models, we aim to identify the cause of the emergence of time-periodic solutions in such Fokker-Planck equations.

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Date/Time : 15 Oct 2021 10:00
Venue : via Zoom
Speaker : Ju Sun, University of Minnesota

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https://nus-sg.zoom.us/j/9775606531?pwd=cVZ6eTRYS3ZzVUlFNXRuSlhMVjJSUT09

Meeting ID: 977 560 6531
Passcode: 123321

Abstract:  Phase retrieval (PR) concerns the recovery of a signal (1D, 2D, or 3D) from its Fourier magnitudes, and is central to numerous areas of scientific imaging. Over the past decade, there have been numerous breakthroughs in understanding simplified or modified versions of the problem, but the existence of effective and robust methods for the original PR problem remains elusive and so theoretical insights are out of the question. In this talk, I will discuss why PR is difficult, the strength and limitation of conventional formulations, the promise and perils of deep learning approaches, as well as our recent methods that solve practical PR problems in an unprecedented regime.

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