UC Berkeley

Mon 4 Feb 2013, 3:10pm
Algebraic Geometry Seminar
ESB 2012

Lattice Poisson AKSZ Theory

ESB 2012
Mon 4 Feb 2013, 3:10pm4:10pm
Abstract
AKSZ Theory is a topological version of the Sigma Model in quantum field theory, and includes many of the most important topological field theories. I will present two generalizations of the usual AKSZ construction. The first is closely related to the generalization from symplectic to Poisson geometry. (AKSZ theory has already incorporated an analogous step from the geometry of cotangent bundles to the geometry of symplectic manifolds.) The second generalization is to phrase the construction in an algebrotopological language (rather than the usual language of infinitedimensional smooth manifolds), which allows in particular for lattice versions of the theory to be proposed. From this new point of view, renormalization theory is easily recognized as the way one constructs strongly homotopy algebraic objects when their strict versions are unavailable. Time permitting, I will end by discussing an application of lattice Poisson AKSZ theory to the deformation quantization problem for Poisson manifolds: a _one_dimensional version of the theory leads to a universal starproduct in which all coefficients are rational numbers.
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Department of Earth and Ocean Sciences, UBC

Tue 5 Feb 2013, 12:30pm
Scientific Computation and Applied & Industrial Mathematics
ESB 4133

Hyperelastic Image Registration: Theory, Numerical Methods, and Applications

ESB 4133
Tue 5 Feb 2013, 12:30pm2:00pm
Abstract
Finding geometrical correspondences between two images, called image registration, is one of the numerous challenging problems in image processing. Commonly, image registration is phrased as a variational problem that is known to be illposed. Thus, regularization is used to ensure existence of solutions, introduce prior knowledge about the expected solution, and/or increase the robustness against noise. This talk gives a comprehensive overview of theory, numerical methods, and applications of regularization energies based on hyperelasticity.
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Georgia Tech

Tue 5 Feb 2013, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB 2012 (in the new PIMS building)

Small BGK waves and Landau damping

ESB 2012 (in the new PIMS building)
Tue 5 Feb 2013, 3:30pm4:30pm
Abstract
In this talk, we discuss the Landau damping  the asymptotic stability of the linearly stable homogeneous states of the VlasovPossion system. It has been proved that solutions to the system linearized at stable homogeneous states decay algebraically in time. In such a Hamiltonian system, this decay is not caused by any dissipation. The nonlinear asymptotic stability is open until recently when Mouhot and Villani proved it of solutions in the Gevery class. The problem in Sobolev spaces remains open. We show that the nonlinear damping does not happen in Sobolev space with too low regularity by constructing BKG waves  traveling waves  arbitrarily close to stable homogeneous states. In the contrary, in Sobolev spaces with higher regularity, we show that there are no invariant structures  including BGK waves  near any stable homogeneous states and thus the same obstacle for the damping as in the rough Sobolev spaces does not appear. Similar results have also been proved for the Euler equation near Couette flow. These are joint works with Zhiwu Lin.
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UBC

Thu 7 Feb 2013, 2:30pm
Symbolic Dynamics and Ergodic Theory Seminar
Math Annex 1102

Computational complexity: a quick overview (Part 1)

Math Annex 1102
Thu 7 Feb 2013, 2:30pm4:00pm
Abstract
In this first of two parts, we will discuss the basic definitions necessary for the study of computability and computational complexity. We will begin by defining the Turing machine model and its limitations in terms of undecidability results. Then, we will introduce some complexity classes such as P and NP, and concepts such as polynomialtime reductions and completeness. Time permitting, some specific combinatorial problems and its relation with statistical physics will be discussed. This talk is a continuation in the informal learning seminar series on Information, Physics and Computation.
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UBC

Thu 7 Feb 2013, 3:30pm
Number Theory Seminar
room MATH 126

On the complexity of primality testing and factorization in algebraic number fields

room MATH 126
Thu 7 Feb 2013, 3:30pm4:30pm
Abstract
I will first review some ideas of algebraic number theory from a computational point of view, and then address the computational complexity of the problems of determining whether an ideal A in the ring of integers of a (fixed) algebraic number field K is prime, and of finding the prime factorization of A. Specifically, I will answer questions of Gil Kalai by giving polynomialtime reductions for the problems of determining whether A is prime and finding the prime factorization of A to the corresponding problems over the rational integers. I will then discuss the problem of factoring an algebraic integer into irreducibles and conclude with the problem of irreducibility testing.
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University of Tennessee, Knoxville

Tue 12 Feb 2013, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB 2012 (in the new PIMS building)

Geometric Inequalities for Hypersurfaces

ESB 2012 (in the new PIMS building)
Tue 12 Feb 2013, 3:30pm4:30pm
Abstract
I will begin this talk by recalling the classic inequalities of AlexandrovFenchel and PolyaSzego for convex surfaces of 3dimensional Euclidean space.
Then, I will present my joint work with Freire, which generalizes the inequalities with rigidity to both a larger class of hypersurfaces and to arbitrary dimensions. I will conclude by mentioning some applications of the results, including a masscapacity inequality for black holes.
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Stanford University

Wed 13 Feb 2013, 3:00pm
Topology and related seminars
ESB 4127

Homological stability for moduli spaces of high dimensional manifolds

ESB 4127
Wed 13 Feb 2013, 3:00pm4:00pm
Abstract
The moduli space of Riemann surfaces M_g parametrizes bundles of genus g surfaces. A classical theorem of J. Harer implies that the homology H_k(M_g) is independent of g, as long as g is large compared to k. In joint work with Oscar RandalWilliams, we establish an analogue of this result for manifolds of higher dimension: The role of the genus g surface is played by the connected sum of g copies of S^n \times S^n.
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UBC

Wed 13 Feb 2013, 3:00pm
Undergraduate Colloquium
MATH 104

Case studies in industrial mathematics

MATH 104
Wed 13 Feb 2013, 3:00pm4:00pm
Abstract
UBC/UMC is the Undergraduate Mathematics Colloquium at UBC. These talks are for undergraduates interested in mathematics and mathematical research. They are put on by professors, senior graduate students and visitors to the department. Graduate students are also invited to attend.
The next talk is by Iain Moyles, a graduate student at the Institute for Applied Mathematics.
Title: Case studies in industrial mathematics
Abstract:
I will present three different projects that highlight a connection between mathematics and industry outside of academia. Each project utilizes a different type of modelling technique and mathematical tool to provide insight into the problem. The aim of my talk is to provide an overview into ways that math taught in the classroom is being used in the "real world" and to highlight important results without presenting too many technical details.
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UBC

Thu 14 Feb 2013, 2:30pm
Symbolic Dynamics and Ergodic Theory Seminar
Math Annex 1102

Computational Complexity

Math Annex 1102
Thu 14 Feb 2013, 2:30pm4:00pm
Abstract
This is a continuation of the talk given on February 7.
This talk is part of the informal learning seminar on
Information, Physics and Computation.
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Tata Institute of Fundamental Research

Thu 14 Feb 2013, 3:30pm
Number Theory Seminar
room MATH 126

Iwasawa theory and residual Galois representations

room MATH 126
Thu 14 Feb 2013, 3:30pm4:30pm
Abstract
Noncommutative Iwasawa theory, especially the noncommutative main conjecture, predicts some congruences between padic Lvalues of elliptic curves, ordinary at a given odd prime p, and having isomorphic residual representations. Some of these results have been proved. On the algebraic side, this should have implications for the algebraic invariants. We shall discuss the theoretic results that can be proved in this framework.
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Cambridge University, University of Memphis

Fri 15 Feb 2013, 3:00pm
SPECIAL
Department Colloquium
Math 125 (reception) MATX 1100 (talk)

Recent Results on Bootstrap Percolation (PIMS/UBC Distinguished Colloquium)

Math 125 (reception) MATX 1100 (talk)
Fri 15 Feb 2013, 3:00pm4:00pm
Abstract
Bootstrap percolation, one of the simplest cellular automata, can be viewed as an oversimplified model of the spread of an infection on a graph. In the past three decades, much work has been done on bootstrap percolation on finite grids of a given dimension in which the initially infected set A is obtained by selecting its vertices at random, with the same probability p, independently of all other choices. The focus has been on the critical probability, the value of p at which the probability of percolation (eventual full infection) is 1/2.
The first half of my talk will be a review of some of the fundamental results concerning critical probabilities proved by Aizenman, Lebowitz, Schonman, Cerf, Cirillo, Manzo, Holroyd and others, and by Balogh, Morris, DuminilCopin and myself. The second half will about about the very recent results I have obtained with Holmgren, Smith, Uzzell and Balister on the time a random initial set takes to percolate.
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Korea Advanced Institute of Science and Technology

Thu 21 Feb 2013, 3:00pm
SPECIAL
Topology and related seminars
ESB 2012

Tabulation of prime knots by arc index

ESB 2012
Thu 21 Feb 2013, 3:00pm4:00pm
Abstract
Every knot can be presented on the union of finitely many half planes which have a common boundary line, so that each half plane contains a single arc of the knot. Such a presentation is called an arc presentation of the knot. The arc index of a knot is the minimal number of half planes needed in its arc presentations.
A grid diagram of a knot is a knot diagram constructed by finitely many vertical line segments and the same number of horizontal line segments such that at each crossing a vertical segment crosses over a horizontal segment. A grid diagram with n vertical segments is easily converted to an arc presentation on n half planes, and vice versa.
Grid diagrams are useful in several ways. A slight modification of a grid diagram gives a front projection of its Legendrian imbedding. Grid diagrams are used to compute Heegaard Floer homology and Khovanov homology.
In this work, we've tabulated prime knots by arc index up to arc index twelve. This is achieved by generating grid diagrams of prime knots up to arc index twelve. This tabulation contains all prime alternating knots up to ten crossings and all prime non alternating knots up to twelve crossings. The largest crossing number among prime knots with arc index twelve is twenty eight.
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McMaster University

Thu 21 Feb 2013, 3:00pm
PIMS Seminars and PDF Colloquiums
University of Calgary, being broadcast in ESB 4127, UBC

PIMS West End Number Theory Seminar: Endoscopic classification of representations for quasisplit unitary groups

University of Calgary, being broadcast in ESB 4127, UBC
Thu 21 Feb 2013, 3:00pm4:00pm
Abstract
We report on the work on endoscopic classification for quasisplit unitary groups.
We will highlight some local and global results that are corollaries of the theory.
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Mathematics, UBC

Mon 25 Feb 2013, 3:00pm
Harmonic Analysis Seminar
Math 126

Rooted Trees and Directional Maximal Operators in \mathbb{R}^3

Math 126
Mon 25 Feb 2013, 3:00pm4:00pm
Abstract
We will explore the L^pboundedness of directional maximal operators in three dimensions. Given a curve on the surface of the sphere, we will describe how the associated set of directions gives rise to a directional maximal operator bounded on all L^p, 1<p<\infty . Extensions of this result to more arbitrary subsets of the sphere given by certain rooted trees will be discussed.
This is joint work with Malabika Pramanik.
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UBC

Mon 25 Feb 2013, 3:10pm
Algebraic Geometry Seminar
ESB 2012

Isotriviality and Descent of Polarized Morphisms

ESB 2012
Mon 25 Feb 2013, 3:10pm4:10pm
Abstract
(joint with A. Bhatnagar)
Suppose that a polarized selfmorphism \phi of X dominates a polarized selfmorphism \psi of Y. Szpiro and Tucker asked if, if \phi is isotrivial, then \psi also descends to an isotrivial morphism. We give an affirmative answer in a large set of cases, including the case Y = P^1. At heart is a result of Petsche, Szpiro, and Tepper on isotriviality and potential good reduction for selfmaps of P^n, which we extend to more general polarized selfmorphisms of projective varieties.
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Tue 26 Feb 2013, 4:00pm
SPECIAL
Graduate Student Center, Room 203

Doctoral Exam

Graduate Student Center, Room 203
Tue 26 Feb 2013, 4:00pm6:00pm
Details
ABSTRACT
Despite a century of study, the macroscopic behaviour of quasistatic granular materials remains poorly understood. In particular, we lack a fundamental system of continuum equations, comparable to the NavierStokes equations for a Newtonian fluid. In this thesis, we derive continuum models for twodimensional granular materials directly from the grain scale, using tools of discrete calculus, which we develop.
To make this objective precise, we pose the canonical isostatic problem: a marginally stable granular material in the plane has 4 components of the stress tensor σ, but only 3 continuum equations in Newton’s laws ∇·σ = 0 and σ = σT. At isostaticity, there is a missing stressgeometry equation, arising from Newton’s laws at the grain scale, which is not present in their conventional continuum form.
We first show that a discrete potential ψ can be defined such that the stress tensor is written as σ = ∇ × ∇ × ψ, where the derivatives are given an exact meaning at the grain scale, and converge to their continuum counterpart in an appropriate limit. The introduction of ψ allows us to understand how force and torque balance couple neighbouring grains, and thus to understand where the stressgeometry equation is hidden.
Using this formulation, we derive the missing stressgeometry equation Δ(F : ∇∇ψ) = 0, introducing a fabric tensor F which characterizes the geometry. We show that the equation imposes granularity in a literal sense, and that on a homogeneous fabric, the equation reduces to a particular form of anisotropic elasticity.
We then discuss the deformation of rigid granular materials, and derive the meanfield phase diagram for quasistatic flow. We find that isostatic states are fluid states, existing between solid and gaseous phases. The appearance of isostaticity is linked to the saturation of steric exclusion and Coulomb inequalities.
Finally, we present a model for the fluctuations of contact forces using tools of statistical mechanics. We find that force chains, the filamentary networks of con tact forces ubiquitously observed in experiments, arise from an entropic instability which favours localization of contact forces.
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Microsoft Research

Wed 27 Feb 2013, 3:00pm
Probability Seminar
ESB 2012

Limiting shape and cuberoot fluctuations of the level lines of (2+1)dimensional SOS

ESB 2012
Wed 27 Feb 2013, 3:00pm4:00pm
Abstract
We give a full description for the shape of the classical (2+1)dimensional SolidOnSolid model above a wall, introduced by Temperley (1952). On an L\times L box at a large inversetemperature \beta the height of most sites concentrates on a single level h = \lfloor \frac1{4\beta}\log L\rfloor for most values of L. For a sequence of diverging boxes the ensemble of level lines of heights (h,h1,\ldots) has a scaling limit in Hausdorff distance iff the fractional parts of \frac1{4\beta}\log L converge to a noncritical value. The scaling limit is explicitly given by nested distinct loops formed via translates of Wulff shapes. Finally, the hlevel lines feature L^{1/3+o(1)} fluctuations from the side boundaries.
Based on joint works with Pietro Caputo, Fabio Martinelli, Allan Sly and Fabio Toninelli.
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BCIT

Wed 27 Feb 2013, 3:00pm
Undergraduate Colloquium
MATH 104

Norms of coining at the Royal Mint and Newton's Revolution

MATH 104
Wed 27 Feb 2013, 3:00pm4:00pm
Abstract
UBC/UMC is the Undergraduate Mathematics Colloquium at UBC. These talks are for undergraduates interested in mathematics and mathematical research. They are put on by professors, senior graduate students and visitors to the department. Graduate students are also invited to attend.
The next talk is by Ari Belenkiy, a mathematician and historian, and a visitor to the Mathematics Department.
Title: Norms of the coining at the Royal Mint and Newton's Revolution
Abstract:
Minting at the Royal Mint includes ten diverse operations organized by the Master to produce coins. Norms were introduced in mid13th century by King Edward I to check on the Master’s overall performance.
From the onset, the remedies were designed to check the statistical mean, i.e., the weight and fineness of the average coin. The actual check was done by sampling from the daily production and estimating deficiency at the public trials, known as the trials of the Pyx. In hindsight, the remedies laid a check on the combination of the mean and a deviation from the mean. This ambiguity, coupled with technological imperfection in a coin’s production, defeated the original purpose of the checks since the variation of coins in weight could not be properly controlled in that era. As a result of inability to control the variation, the remedies were set unreasonably wide.
With the advent of a civil society in Britain in the 17th century, together with rise of transparency and accountability in state institutions, the remedies began serving another purpose – to ascertain the quality of coining. This became especially urgent at the turn of the 18th century, when a large variation in weight of the gold coins led bankers and goldsmiths to cull heavy pieces out of circulation and recoin them to their advantage.
In 1719, Sir Isaac Newton claimed to have stopped the practice of culling in Great Britain, thus “saving some thousands of pounds to the Crown.” By improving the minting procedure, he reduced the variation of coins in weight. Judging from the extant statistical data preserved in the Jury Verdicts written from the late 17th century on, he saved the Crown about £40,000.
Moreover, Newton tightened the norms of coins’ admissibility: beginning in 1707, a small sample of coins was tested at each trial, effectively reducing the margin (remedy in weight).
If time permits we shall discuss the postNewton progress of coining in Great Britain till modern times, presenting the standard deviation of coins in weight as a measure of the technological advance of the country. We shall also pose some open questions.
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Dept of Mechanical & Industrial Engineering, and Institute of Biomaterials & Biomedical Engineering, Univ. of Toronto

Thu 28 Feb 2013, 2:00pm
Mathematical Biology Seminar
ESB 4133

Bone cell mechanotransduction

ESB 4133
Thu 28 Feb 2013, 2:00pm3:00pm
Abstract
Bone remodeling involves the coupled action of osteoblasts and osteoclasts. Osteocytes are believed to sense and respond to mechanical loading applied to bone at the tissue level and regulate bone remodeling process. However, how osteocytes regulate the action of osteoblasts and osteoclasts is unknown. To systematically investigate the cellular level mechanism underlying the osteocyte mechanoregulation of bone remodeling, we applied different types of mechanical stimuli to osteocytes. Cellcell communications and bone formation and bone resorption markers at transcriptional level and protein level were analyzed. We found those osteocytes are highly responsive to dynamic fluid flow, dynamic hydraulic pressure, and low magnitude and high frequency vibration. Our data indicate that mechanically challenged osteocytes release soluble factors promote bone formation and inhibit bone resorption.
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UBC

Thu 28 Feb 2013, 2:30pm
Symbolic Dynamics and Ergodic Theory Seminar
Math Annex 1102

Computational complexity (part 3)

Math Annex 1102
Thu 28 Feb 2013, 2:30pm4:00pm
Abstract
This is a continuation of previous seminars on Feb. 7 and 14. This talk will focus on classes of algorithms
and in particular on algorithms for approximate counting.
These talks are part of the informal learning seminar on Information, Physics and Computation.
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ENS de Lyon

Thu 28 Feb 2013, 3:00pm
Number Theory Seminar
room MATH 126

The padic local Langlands correspondence and LubinTate groups

room MATH 126
Thu 28 Feb 2013, 3:00pm3:50pm
Abstract
I will recall the important features of the padic local Langlands correspondence for GL_{2}(Q_{p}). Extending this correspondence to other groups seems to require doing padic Hodge theory in a slightly different way. I will explain the new features that arise when one does this, in the simplest setting.
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Mathematisches Institut der Universität Heidelberg

Thu 28 Feb 2013, 4:10pm
Number Theory Seminar
room MATH 126

Functorial properties of determinant functors  with applications to the local Tamagawa number conjecture

room MATH 126
Thu 28 Feb 2013, 4:10pm5:00pm
Abstract
We explain the compatibility of determinant functors with spectral sequences and apply it to descent calculations in local Iwasawa theory related to the εisomorphism conjecture of Fukaya and Kato.
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Note for Attendees
Pizza and pop provided.