Colloquiums and Public Lectures

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2018

17 December 2018 Title: Mathematical deep learning for drug discovery

Date:  17 December 2018 (Monday) 

Time:  10.30am to 11.30am

Venue:  MAS Executive Classroom 2, MAS-03-07
             School of Physical and Mathematical Sciences

Speaker : Professor Guowei Wei
                Department of Mathematics 
                Michigan State University, USA

Abstract: Designing efficient drugs for curing diseases is of essential importance for the 21st century's life science. Computer-aided drug design and discovery has obtained a significant recognition recently. However, the geometric complexity of protein-drug complexes remains a grand challenge to conventional computational methods, including machine-learning algorithms. We assume that the intrinsic physics of interest of protein-drug complexes lies on low-dimensional manifolds or subspaces embedded in a high-dimensional data space. We devise topological abstraction, geometric simplification, graph reduction, and multiscale modeling to encode high-dimensional, massive and diverse biological data into low-dimensional representations. These representations are integrated with advanced deep learning algorithms for the predictions of protein-ligand binding affinity, drug toxicity, drug solubility, drug partition coefficient and mutation induced protein stability change, and for the discrimination of active ligands from decoys. I will briefly discuss how this approach became the top performer in D3R Grand Challenges, a worldwide competition series in computer-aided drug design and discovery (http://users.math.msu.edu/users/wei/D3R_GC3.pdf).

Host: Division of Mathematical Sciences, School of Physical and Mathematical Sciences
03 December 2018
Title: Lie group and homogeneous space variational integrators applied to geometric optimal control theory

Date:  3 December 2018 (Monday)

Time:  4.00pm to 5.00pm

Venue: Lecture Theatre 4 (SPMS-03-09)

Speaker : Professor Melvin Leok
Department of Mathematics
University of California, San Diego

Abstract:  The geometric approach to mechanics serves as the theoretical underpinning of innovative control methodologies in geometric control theory. These techniques allow the attitude of satellites to be controlled using changes in its shape, as opposed to chemical propulsion, and are the basis for understanding the ability of a falling cat to always land on its feet, even when released in an inverted orientation.
We will discuss the application of geometric structure-preserving numerical schemes to the optimal control of mechanical systems. In particular, we consider Lie group variational integrators, which are based on a discretization of Hamilton's principle that preserves the Lie group structure of the configuration space. In contrast to traditional Lie group integrators, issues of equivariance and order-of-accuracy are independent of the choice of retraction in the variational formulation. The importance of simultaneously preserving the symplectic and Lie group properties is also demonstrated .
Recent extensions to homogeneous spaces yield intrinsic methods for Hamiltonian flows on the sphere, and have potential applications to the simulation of geometrically exact rods, structures and mechanisms. Extensions to Hamiltonian PDEs and uncertainty propagation on Lie groups using noncommutative harmonic analysis techniques will also be discussed.
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Host: Professor Bernhard Schmidt
          Division of Mathematical Sciences, School of Physical and Mathematical Sciences
26 September 2018 Title: The beauty of mathematics shows itself to patient followers: The work of Maryam Mirzakhani

Date: 
26 September 2018

Time:  1.30pm to 2.30pm

Venue: Lecture Theatre 2 (SPMS-03-03)

Speaker: Dr Daniel Mathews
School of Mathematical Sciences
Monash University

Abstract: Maryam Mirzakhani was a brilliant, trailblazing mathematician, and the first woman to win a Fields Medal. She proved many incredible theorems across a range of fields on the cutting edge of pure mathematics. She was also an all-round excellent human being. Tragically, she passed away last year at the age of 40. In this talk I will discuss her life and work, and attempt to explain some of her mathematics and its implications. Along the way we'll see such things as moduli spaces, hyperbolic surfaces, the art of MC Escher, and fun facts about billiards. I will not assume any technical knowledge of these fields.

Host:  Associate Professor Andrew James Kricker
Division of Mathematical Sciences, School of Physical and Mathematical Sciences
14 September 2018 Title: Data-Driven Approach to Pricing Optimization

Date: 14 September 2018 (Friday)

Time: 1.30pm to 2.30pm

Venue: Lecture Theatre 3 (SPMS-03-02)

Speaker:  Dr Yan Zhenzhen
Division of Mathematical Sciences
School of Physical and Mathematical Sciences

Abstract: We have developed an estimation and optimization framework for the multi-product pricing problem and network pricing problem. The key feature is to develop a convex model to approximate customer’s choice response to the change of prices. The convex model exploits properties of the marginal distributions of the random shock in customer’s utility function. We have shown that the multi-product pricing problem becomes a convex optimization problem with the proposed choice model under a log-concavity assumption of each marginal probability density function. With this approach, we used aggregate sales information from a set of pricing experiments to guide us to the appropriate consumer choice model without presuming a structural choice model. This has partially addressed the problem of model misspecification for pricing problems. Extensive tests using both simulated and experimental data for two companies' multi-product pricing problems demonstrates clearly the benefits of the data driven pricing approach.

Host: Division of Mathematical Sciences, School of Physical and Mathematical Sciences
29 June 2018  Title: Stories vs Statistics

Date: 29 June 2018 (Friday)

Time: 4.00pm to 5.00pm

Venue: Public Lecture : Lecture Theatre 4 (SPMS-03-09)
           
Speaker : Professor John Allen Paulos
                PhD (University of Wisconsin in Madison)
                USA

Abstract:  The talk will discuss the complex relationship between stories and statistics or, to vary the alliteration, between narratives and numbers. It will then go on to the most common mathematical mistakes in news reports and the media generally. 

No mathematical background will be needed, just a bit of arithmetic, a little logic, and maybe a feel for probability. The talk is in two parts, the first a bit more theoretical, the second more topical and news-related.

Host: Division of Mathematical Sciences, School of Physical and Mathematical Sciences

28 February 2018
Title: Branching diffusion representation for nonlinear Cauchy problems and Monte Carlo approximation
 
Date: 28 February 2018 (Wednesday)

Time: 1.30pm to 2.30pm

Venue: Lecture Theatre 4 (SPMS-03-09) 
School of Physical and Mathematical Sciences
 
Speaker: Professor Nizar Touzi
Ecole Polytechnique
France
 
Abstract:
We provide a probabilistic representations of the solution of some semilinear hyperbolic and high-order PDEs based on branching diffusions. These representations pave the way for a Monte-Carlo approximation of the solution, thus bypassing the curse of dimensionality. We illustrate the numerical implications in the context of some popular PDEs such as the Burger's equation, the nonlinear Klein-Gordon equation, a simplified scalar version of the Yang-Mills equation, a fourth-order nonlinear beam equation and the Gross-Pitaevskii PDE as an example of nonlinear Schrödinger equations.
Speaker Biography:
Nizar Touzi is Professor of Applied Mathematics at Ecole Polytechnique (France) since 2006. He was previously Chair Professor at Imperial College London. He was an invited session speaker at the International Congress of Mathematicians (Hyderabad 2010). He received the Louis Bachelier prize of the French Academy of Sciences in 2012, the Paris Europlace prize of Best Young Researcher in Finance in 2007, and is presently holding an Advanced ERC grant 2013-2018. He is Co-editor and Associate Editor in various international journals in the fields of financial mathematics, applied probability, and control theory.
 
Host: Associate Professor Nicolas Privault
Division of Mathematical Sciences, School of Physical and Mathematical Sciences
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