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 Events
UBC Zoology and Mathematics
Mon 15 Sep 2014, 3:00pm
Institute of Applied Mathematics
LSK 460
Evolutionary Dynamics in High-Dimensional Phenotype Spaces
LSK 460
Mon 15 Sep 2014, 3:00pm-4:00pm

Abstract

Adaptive dynamics is a general framework to study long-term evolutionary dynamics. It is typically used to study evolutionary scenarios in low-dimensional phenotype spaces, such as the important phenomenon of evolutionary branching (adaptive diversification). I will briefly recall the basic theory of evolutionary branching and present a well-studied empirical example. Because birth and death rates of individuals are likely to be determined by many different phenotypic properties, it is important to consider evolutionary dynamics in high-dimensional phenotype spaces. I will present some results about evolutionary branching in high-dimensional phenotype spaces, as well as results about more general types of non-equilibrium evolutionary dynamics, such as chaos. Finally, I will compare the deterministic adaptive dynamics in high-dimensional phenotype spaces to individual-based simulations of the underlying stochastic birth-death process.
 

Note for Attendees

Michael Doebeli is the winner of the 2014 CAIMS Research Prize. 
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Mainz
Mon 15 Sep 2014, 3:00pm
CRG Geometry and Physics Seminar
ESB 4127 (host: UBC)
Canonical Coordinates from Tropical Curves
ESB 4127 (host: UBC)
Mon 15 Sep 2014, 3:00pm-4:00pm

Abstract

Morrison defined canonical coordinates near a maximal degeneration point in the moduli of Calabi-Yau manifolds using Hodge theory. Gross and Siebert introduced a logarithmic-tropical algorithm to provide a canonically parametrized smoothing of a degenerate Calabi-Yau. We show that the Gross-Siebert coordinate is a canonical coordinate in the sense of Morrison. The coordinates are given by period integrals which we compute explicitly integrating over cycles constructed using tropical geometry. This is joint work with Siebert.

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Rustum Choksi
Department of Mathematics and Statistics, McGill University
Tue 16 Sep 2014, 12:30pm
Scientific Computation and Applied & Industrial Mathematics
ESB 4133 (PIMS Lounge)
Self-Assemby: Variational Models and Energy Landscapes
ESB 4133 (PIMS Lounge)
Tue 16 Sep 2014, 12:30pm-1:30pm

Abstract

Self-assembly, a process in which a disordered system of preexisting components forms an organized structure or pattern, is both ubiquitous in nature and important for the synthesis of many designer materials. In this talk, we will address two variational paradigms for self-assembly from the point of view of analysis and computation. The first variational model is a nonlocal perturbation (of Coulombic-type) to the well-known Ginzburg-Landau/Cahn-Hilliard free energy. The functional has a rich and complex energy landscape with many metastable states. We present recent joint work with Dave Shirokoff (NJIT) and J.C. Nave (McGill) on developing a method for assessing whether or not a particular (computed) metastable state is a global minimizer. Our method is based upon a very simple idea of using a ``suitable" global convex envelope of the energy. We present full details for global minimality of the constant state, and then present a few partial results on the application to non-constant, computed metastable states.
 
The second variational model is purely geometric and finite-dimensional: Centroidal Voronoi Tessellations (CVT) of rigid bodies. Using a level set formulation, we a priori fix the geometry for the structures and consider self-assembly entirely dictated by distance functions. We introduce a novel fast algorithm for simulating CVTs of rigid bodies in any space dimension. The method allows us to empirically explore the CVT energy landscape. This is joint work with Lisa Larsson (Courant) and J.C. Nave (McGill).
 
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John Ma
UBC
Tue 16 Sep 2014, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB 2012
Singularities in Lagrangian Mean Curvature Flow
ESB 2012
Tue 16 Sep 2014, 3:30pm-4:30pm

Abstract

Lagrangian Mean Curvature Flow (LMCF) is a geometric flow, aiming to deform a Lagrangian immersion to a minimal one. To understand the flow, it is important to understand the formation of singularity in LMCF. In this talk, I will introduce the concept of a self-shrinker (a local model for singularity), how it is formed in LMCF, and give some examples of Lagrangian self-shrinkers. Then I will discuss a recent work with Jingyi Chen concerning the space of all compact Lagrangian self-shrinkers in \mathbb C^2.
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University of Washington
Tue 16 Sep 2014, 4:00pm
Discrete Math Seminar
ESB 4133
Coxeter-Knuth Graphs and a signed Little map
ESB 4133
Tue 16 Sep 2014, 4:00pm-5:00pm

Abstract

We propose an analog of the Little map for reduced expressions for signed permutations. We show that this map respects the transition equations derived from Chevellay's formula on Schubert classes. We discuss many nice properties of the signed Little map which generalize recent work of Hamaker and Young in type A where they proved Lam's conjecture.   As a key step in this work, we define shifted dual equivalence graphs building on work of Assaf and Haiman and prove they can be characterized by axioms.   These graphs are closely related to both the signed Little map and to the Coxeter-Knuth relations of type B due to Kraskiewicz.
 
This talk is based on joint work with Zach Hamaker, Austin Roberts and Ben Young.
 
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National University of Mexico
Thu 18 Sep 2014, 2:15pm SPECIAL
Topology and related seminars
ESB 4133
On the Chern classes of singular varieties
ESB 4133
Thu 18 Sep 2014, 2:15pm-3:15pm

Abstract

Chern classes of complex manifolds play a key role in geometry and topology. In this talk we shall discuss how these classes extend to singular varieties. In fact there are various possible extensions, depending on which properties of Chern classes you want to preserve. This is closely related to asking who plays the role of the tangent bundle at the singular points (where there is no tangent bundle).
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Hebrew University of Jerusalem
Thu 18 Sep 2014, 3:30pm
Number Theory Seminar
room MATH 126
From Ramanujan graphs to Ramanujan complexes
room MATH 126
Thu 18 Sep 2014, 3:30pm-4:30pm

Abstract

Ramanujan graphs are optimal expanders (from spectral point of view). Explicit constructions of such graphs were given in the 80's as quotients of the Bruhat-Tits tree associated with GL(2) over a local field F, by suitable congruence subgroups. The spectral bounds were proved using works of Hecke, Deligne and Drinfeld on the "Ramanujan conjecture" in the theory of automorphic forms. The work of Lafforgue, extending Drinfeld from GL(2) to GL(n), opened the door for the construction of Ramanujan complexes as quotients of the Bruhat-Tits buildings. This gives finite simplical complxes which on one hand are "random like" and at the same time have strong symmetries. Recently various applications have been found in combinatorics, coding theory and in relation to Gromov's overlapping properties. We will describe these developments and give some details on recent applications. 
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Hebrew University of Jerusalem
Fri 19 Sep 2014, 3:00pm
Department Colloquium
ESB 2012 (PIMS)
High dimensional expanders and Ramanujan complexes (PIMS-UBC Distinguished Colloquium)
ESB 2012 (PIMS)
Fri 19 Sep 2014, 3:00pm-4:00pm

Abstract

Expander graphs have played, in the last few decades, an important role in computer science, and  in the last decade, also in pure mathematics.  In recent years a theory of "high-dimensional expanders" is starting to emerge - i.e., simplical complexes which generalize various properties of expander graphs. This has some geometric motivations (led by Gromov) and combinatorial ones (started by Linial and Meshulam).  The talk will survey the various directions of research and their applications, as well as potential applications in math and CS.  Some of these lead to questions about buildings and representation theory of p-adic groups.
                  We will survey the work of a number of people. The works of the speaker in this direction are with various subsets of  { S. Evra, K. Golubev,  T. Kaufman,  D. Kazhdan , R. Meshulam, S. Mozes }
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