Date/Time : 03 Nov 2021 16:00
Venue : via Zoom
Speaker : Wu Guohua, Nanyang Technological University

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

Abstract:   Domain theory was contrived by Dana Scott in 1969 as a theory of approximating computations. This topic was also raised by Ershov independently. In this talk, I will give a brief introduction of domain theory first, hopefully, from the beginning, and then move to the comparison of various substitutions of Hausdorff property, including sobriety, well-filteredness and monotone convergence.

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Date/Time : 01 Nov 2021 10:00
Venue : via Zoom
Speaker : Yingzhou Li, Fudan University

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https://nus-sg.zoom.us/j/86776918257?pwd=cHJ3eDZNclUweWhBaitPZFRieGtNQT09

Meeting ID: 867 7691 8257
Passcode: 061477

Abstract: Coordinate descent methods are considered for eigenvalue problems based on a reformulation of the leading eigenvalue problem as a nonconvex optimization problem. The convergence of several deterministic coordinate methods is analyzed and compared. We also analyze the global convergence property of coordinate gradient descent with random choice of coordinates and stepsizes. Under generic assumptions, we prove that the algorithm iterate will almost surely escape strict saddle points of the objective function. As a result, the algorithm is guaranteed to converge to local minima if all saddle points are strict. Numerical examples of applications to quantum many-body problems demonstrate the efficiency and provide benchmarks of the proposed coordinate descent methods.

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Date/Time : 29 Oct 2021 09:00
Venue : via Zoom
Speaker : Luca Spolaor, University of California San Diego

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https://nus-sg.zoom.us/j/86945333380?pwd=Q0VEM2drc0YrKzFUc3VHbFVqNjRCQT09

Meeting ID: 869 4533 3380
Passcode: 583463

Abstract:  In this talk I will discuss some results about isolated singularities of minimal surfaces arising from minimization and Min-Max. In particular, I will focus on the local description of minimal surfaces at such singularities and on their generic behavior with respect to a change in the ambient metric.

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Date/Time : 29 Oct 2021 10:00
Venue : via Zoom
Speaker : Jian Tang, Mila-Quebec Al Institute

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

Meeting ID: 977 560 6531
Passcode: 123321

Abstract:  Drug discovery is a very long and expensive process, taking on average more than 10 years and costing $2.5B to develop a new drug. Artificial intelligence has the potential to significantly accelerate the process of drug discovery by extracting evidence from a huge amount of biomedical data and hence revolutionizes the entire pharmaceutical industry. In particular, graph representation learning and geometric deep learning–a fast growing topic in the machine learning and data mining community focusing on deep learning for graph-structured and 3D data—has seen great opportunities for drug discovery as many data in the domain are represented as graphs or 3D structures (e.g. molecules, proteins, biomedical knowledge graphs). In this talk, I will introduce our recent progress on geometric deep learning for drug discovery and also a newly released open-source machine learning platform for drug discovery, called TorchDrug.

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Date/Time : 28 Oct 2021 16:00
Venue : via Zoom
Speaker : Kunlun Qi, The Chinese University of Hong Kong

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https://nus-sg.zoom.us/j/81670327104?pwd=RnJwRm9rblhuYkRZS1dlY1NvOU91Zz09

Meeting ID: 816 7032 7104
Passcode: 779661

Abstract:  Numerical approximation of the Boltzmann equation is a challenging problem due to its high-dimensional, nonlocal, and nonlinear collision integral. Over the past decade, the Fourier-Galerkin spectral method has become a popular deterministic method for solving the Boltzmann equation, manifested by its high accuracy and potential of being further accelerated by the fast Fourier transform. Albeit its practical success, the stability of the method is only recently proved by utilizing the “spreading” property of the collision operator. In this talk, we introduce a new proof based on a careful $L^2$ estimate of the negative part of the solution. We also discuss the applicability of the result to various initial data, including both continuous and discontinuous functions. This talk is based on some joint works with Tong Yang (CityU) and Jingwei Hu (UW).

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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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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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