The Third International Conference on Mathematics and Statistics

Philip K. Maini
University of Oxford , UK

Biography

Philip K. Maini received his Bachelor of Arts in Mathematics from Balliol College, Oxford, UK in 1982 and his DPhil in 1985 under the supervision of Professor J.D. Murray, FRS.  In 1988 he was appointed Assistant Professor in the Mathematics Department at the University of Utah, Salt Lake City, USA. In 1990, he returned to Oxford as a University Lecturer and, in 1998, was appointed Professor of Mathematical Biology by Recognition of Distinction and Director of the Wolfson Centre for Mathematical Biology. In 2005, he was appointed Statutory Professor of Mathematical Biology. He is on the editorial boards of a large number of journals, including serving as Editor-in-Chief of the Bulletin of Mathematical Biology (2002–15). He is a SIAM Fellow, Fellow of the Royal Society (FRS), Fellow of the Academy of Medical Sciences (FMedSci), and Foreign Fellow of the Indian National Science Academy (FNA).

His present research projects include the modelling of avascular and vascular tumors, normal and abnormal wound healing, and a number of applications of mathematical modelling in pattern formation in early development, as well as the theoretical analysis of the mathematical models that arise in all these applications. 

He co-authored with Jonathan Sherratt and Paul Dale a Bellman Prize-winning paper (1997), was awarded a Royal Society Leverhulme Trust Senior Research Fellowship for 2001-2 and a Royal Society-Wolfson Research Merit Award (2006–11). In 2009, he was awarded the LMS Naylor Prize and Lectureship and in 2014 he was listed in "The World's Most Influential Scientific Minds 2014" (Thomson Reuters). In 2017, he was awarded the Arthur T. Winfree Prize from the Society of Mathematical Biology (SMB).

Abstract

Modelling Collective Cell Migration
Collective cell migration is a very common phenomenon in biology, occurring in embryology, wound healing and disease (cancer). This talk will review our recent work in two areas: (i) angiogenesis—the process by which new blood vessels are created by tumor cells. We will derive a new model for this phenomenon in the form of a coupled system of fully nonlinear partial differential equations. We will

compare its behavior with that of an existing model in the literature; (ii) cranial neural crest migration—we develop a simple agent-based model for this process and show how it can be used to generate new insights into the biology of this fundamental developmental process.

Richard A. Brualdi
University of Wisconsin–Madison, USA

Biography

Richard A. Brualdi is UWF Beckwith Bascom Professor of Mathematics 2004-2008 (now emeritus) at the University of Wisconsin-Madison, USA. He received the Chancellor's Award for Excellence in Teaching at UW-Madison in 1986. In 2000, he received the Euler Medal for a lifetime career of distinguished contributions to combinatorial research by a member of the

Institute of Combinatorics and its Applications (ICA). In 2005, he received the International Linear Algebra (ILAS) Prize for lifetime contributions.

He is a fellow of the Society for Industrial and Applied Mathematics (SIAM) and Fellow of the American Mathematical Society (AMS). He is a co-editor-in-chief of the journal Linear Algebra and Its Applications and a co-editor-in-chief of the Electronic Journal of Combinatorics. He is the author of more than 200 papers and six books. He has had 37 PhD students at the University of Wisconsin-Madison.

Abstract

Permutation (Matrices) and Beyond
Permutations are one of the most basic concepts in mathematics. Their study is both ancient and modern. They can be viewed as the integers 1,2,…,n in some order or as n×n permutation matrices. They can be regarded as data which is to be sorted. The explicit definition of the classical determinant uses permutations. Associated with a permutation is the notion of an inversion (or interchange) where a larger integer precedes a smaller integer. Inversions can be used to define two partial orders on permutations, one weaker than the other. Partial orders have a unique minimal completion to a lattice, the Dedekind-MacNeille completion.

Generalizations of permutation matrices determine related matrix classes. One of the above-mentioned partial orders gives rise to the generalization called alternating sign matrices (ASMs) that arose independently in the mathematics and physics literature. Permutations may contain certain patterns, e.g., three integers in increasing order; avoiding such patterns determines certain permutation classes. Similar restrictions can be placed more generally on (0,1)-matrices. The convex hull of n×n permutation matrices is the polytope of n×n doubly stochastic matrices. In a similar way, we get ASM polytopes. The purpose of this lecture is to explore these and other ideas and their connections.