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 Events
Brian Marcus
UBC
Tue 1 May 2012, 2:00pm
Symbolic Dynamics and Ergodic Theory Seminar
Math 126
Theomodynamic Formalism I
Math 126
Tue 1 May 2012, 2:00pm-3:30pm

Abstract

We will give an overview of Ruelle's book, Thermodynamic Formalism. On May 1 and 3, we plan to cover Chapter 0, interspersing examples with Ruelle's abstract treatment We will relate the subject to material covered in the Entropy course, Math 601D (Fall, 2011):

http://www.math.ubc.ca/~marcus/math601D.

Familiarity with entropy will be helpful, but concepts will be reviewed.  This will be the first of 10 informal seminars on the subject, through the month of May, given by the participants. 



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UBC
Wed 2 May 2012, 11:30am
Algebraic Groups and Related Structures
Math 126
An intro to categories fibered in groupoids
Math 126
Wed 2 May 2012, 11:30am-1:00pm

Abstract

This is the first talk in a series where we'll define fibered categories, quotient stacks, and gerbes banded by commutative groups. We'll also discuss essential and canonical dimension of fibered categories and some applications to the essential dimension of algebraic groups.

In this first talk, we'll define fibered categories and categories fibered in groupoids (CFGs). We'll also discuss examples and introduce quotient stacks as a CFG.

The only prerequisites are basic category theory and basic algebraic geometry. No prior knowledge of stacks, essential dimension, etc. is needed.
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Warwick
Wed 2 May 2012, 3:00pm
Probability Seminar
MATH 126
Probabilistic approaches to symmetrised many-particle systems
MATH 126
Wed 2 May 2012, 3:00pm-4:00pm

Abstract

We consider a symmetrised functional of Brownian bridges, which is related to the partition function of an interacting many-particle system. The aim is to calculate the associated free energy in the thermodynamic limit where temperature and particle density remain positive. More precisely, we give a lower and upper bound on the free energy in terms of certain variational principles. The bounds coincide if either temperature is fixed and the particle density is small or conversely if the density remains fixed and the temperature is high. The novel idea  is a representation of the partition function in terms of a marked point process, where the marks are Brownian bridges starting and ending at the corresponding points of the point process. Based on the large deviations results for marked point processes, we employ an argument analogously to Varadhan's lemma to eventually obtain the bounds on the partition function. The difference in upper and lower bounds, however, is not merely technical, but hints at the emergence of Bose-Einstein condensation, where infinitely long cycles appear and whose description remains a major challenge of the field. In a second part we outline the connection to random permutation and random partitions models.

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Brian Marcus
UBC
Thu 3 May 2012, 2:00pm
Symbolic Dynamics and Ergodic Theory Seminar
Math 126
Theomodynamic Formalism II
Math 126
Thu 3 May 2012, 2:00pm-3:30pm

Abstract


Continuation of May 1 seminar.
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Stefan Adams
University of Warwick
Tue 8 May 2012, 2:00pm
Symbolic Dynamics and Ergodic Theory Seminar
Math 126
Thermodynamic Formalism III
Math 126
Tue 8 May 2012, 2:00pm-3:30pm

Abstract

 
Continuation of this introductory series, with emphasis on the Ising model. 
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UBC
Wed 9 May 2012, 11:30am
Algebraic Groups and Related Structures
Math 126
An intro to categories fibered in groupoids
Math 126
Wed 9 May 2012, 11:30am-1:00pm

Abstract

 This is the second talk in a series where we'll define fibered categories, quotient stacks, and gerbes banded by commutative groups. We'll also discuss essential and canonical dimension of fibered categories and some applications to the essential dimension of algebraic groups.
 
In this second talk, we'll define and describe the quotient stack X/G for an algebraic group G and a G-scheme X.
 
The only prerequisites are basic category theory and basic algebraic geometry. No prior knowledge of stacks, essential dimension, etc. is needed.
 
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Tom Meyerovitch
UBC
Thu 10 May 2012, 2:00pm
Symbolic Dynamics and Ergodic Theory Seminar
Math 126
Thermodynamic Formalism IV: Gibbs states
Math 126
Thu 10 May 2012, 2:00pm-3:30pm

Abstract

 
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Felipe Garcia
UBC
Tue 15 May 2012, 2:00pm
Symbolic Dynamics and Ergodic Theory Seminar
Math 126
Theomodynamic Formalism V: The Variational Principle
Math 126
Tue 15 May 2012, 2:00pm-3:30pm

Abstract


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Peter Hydon
University of Surrey, UK
Tue 15 May 2012, 3:00pm
Symmetries and Differential Equations Seminar
Math Annex 1118
Conservation laws of difference equations
Math Annex 1118
Tue 15 May 2012, 3:00pm-4:00pm

Abstract

Given a partial difference equation (PDiffE), how can one find its conservation laws? Indeed, what is a conservation law? These questions have fairly simple answers for partial differential equations (PDEs), but are harder for PDiffEs. However, recent work has shown that similarities in the key algebraic structures for PDEs and PDiffEs can be exploited. In particular, there are difference analogues of Noether's first and second theorems. Furthermore, each class of conservation laws is characterized by a function, from which the components of the conservation law may be reconstructed. This function is used: a) to establish the converse of Noether's Theorem, b) to prove that infinite hierarchies of inequivalent conservation laws exist for certain integrable PDiffEs, c) to construct finite difference schemes that preserve multiple (non-hyperbolic) conservation laws.

This talk is suitable for a general mathematical audience.
 
Peter Hydon is well known for his 2000 Cambridge Text in Applied Mathematics: Symmetry Methods for Differential Equations: A Beginner's Guide
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UBC
Wed 16 May 2012, 11:30am
Algebraic Groups and Related Structures
Math 126
An intro to categories fibered in groupoids
Math 126
Wed 16 May 2012, 11:30am-1:00pm

Abstract

We'll review the definitions of gerbes banded by C and quotient stacks.
Then, I'll define canonical and essential dimension, with examples. I'll
prove two results relating essential/canonical dimension of gerbes/quotient
stacks/algebraic groups. I'll finish by briefly explaining how Karpenko and
Merkurjev used these ideas to prove results about the essential dimension
of finite p-groups.
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T.C. Scott
University of Waterloo, Ontario and University of Aachen, Germany
Thu 17 May 2012, 11:00am SPECIAL
One Time Event
Math Annex 1102
Mathematical Physics Seminar: Molecular Physics, Gravity and the Lambert Function
Math Annex 1102
Thu 17 May 2012, 11:00am-12:00pm

Details

The impetus arose from the fact that complete analytical solutions for the metric of a covariant N-body system have proven elusive in General Relativity.  To simplify the problem, the number of dimensions was lowered to (1+1) namely one spatial dimension and one-time dimension.  This model problem, known as R=T theory (as opposed to the general G=T theory) is amenable to exact solutions in terms of a generalization of the Lambert W function.  It was also found that the field equation governing the dilaton (derived from differential geometry) was none other than the Schrodinger equation and consequently amenable to quantization.  Thus, one had a theory which combined gravity, quantization and even the electromagnetic interaction.  The outcome revealed a previously unknown and already existing natural link between general relativity and quantum mechanics.
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Nishant Chandgotia
UBC
Thu 17 May 2012, 2:00pm
Symbolic Dynamics and Ergodic Theory Seminar
Math 126
Theomodynamic Formalism VI: Relation between Gibbs states and Equilibrium states
Math 126
Thu 17 May 2012, 2:00pm-3:30pm

Abstract


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Robert Israel
UBC
Tue 22 May 2012, 2:00pm
Symbolic Dynamics and Ergodic Theory Seminar
Math 126
Thermodynamic Formalism VII: Consequences of Convexity
Math 126
Tue 22 May 2012, 2:00pm-3:30pm

Abstract


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UBC
Wed 23 May 2012, 11:30am
Algebraic Groups and Related Structures
Math 126
A word on Grothendieck topologies
Math 126
Wed 23 May 2012, 11:30am-1:00pm

Abstract

We will define a few Grothendieck topologies and what is a torsor is in each of these topologies. This is in preparation to talk about the various cohomology theories these topologies define. We shall also define the Grothendieck-Brauer group and the cohomological Brauer group and go over their basic properties.
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Brett Kolesnik
UBC
Thu 24 May 2012, 10:00am
Symbolic Dynamics and Ergodic Theory Seminar
Math 126
Thermodynamic Formalism VIII: Entropy of Domino Tiling
Math 126
Thu 24 May 2012, 10:00am-10:30am

Abstract


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Harvard University
Thu 24 May 2012, 3:00pm SPECIAL
Department Colloquium
Math 100
2012 Niven Lecture: On growth and form: geometry, physics and biology
Math 100
Thu 24 May 2012, 3:00pm-4:00pm

Abstract

 The diversity of form in living beings led Darwin to state that it is "enough to drive the sanest man mad". How can we describe this variety? How can we predict it?  Motivated by biological observations on different scales from molecules to tissues, I will show how a combination of biological and physical experiments, mathematical models and simple computations allow us to begin to unravel the physical basis for morphogenesis.

About the Niven Lectures: Ivan Niven was a famous number theorist and expositor; his textbooks have won numerous awards and have been
translated into many languages.  They are widely used to this day. Niven was born in Vancouver in 1915, earned his Bachelor's and Master's
degrees at UBC in 1934 and 1936 and his Ph.D. at the University of Chicago in 1938. He was a faculty member at the University of Oregon since 1947 until his retirement in 1982. The annual Niven Lecture, held at UBC since 2005, is funded in part through a generous bequest from
Ivan and Betty Niven to the UBC Mathematics Department.

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UBC
Mon 28 May 2012, 12:30pm SPECIAL
One Time Event
MATX 1100 (talk)
Graduation Reception (Math 125 at 12:30 pm)
MATX 1100 (talk)
Mon 28 May 2012, 12:30pm-3:00pm

Details

The Graduation Reception is held at 12:30-2:00 pm in the MATH building, room MATH 125. 
The lecture begins at 2:00-3:00 pm in the Math Annex building, room MATX 1100.  Everyone is welcome to attend both events.

Special Lecture by Malabika Pramanik.
Title: Needles, bushes, hairbrushes and trees

Abstract:  Points, lines and circles are among the most primitive and fundamental of mathematical concepts, yet few geometric objects have generated more beautiful and nontrivial mathematics. Deceptively simple in their formulation, many classical problems involving sets of lines or circles remain open to this day. I will begin with a sample that has spearheaded much of modern research, and explore connections with analysis, geometry, combinatorics and probability.  By the end, we will have seen applications in physics and computer science, and maybe in the not-too-distant future, parallel parking?



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Tyler Helmuth
UBC
Tue 29 May 2012, 2:00pm
Symbolic Dynamics and Ergodic Theory Seminar
Math 126
Thermodynamic Formalism IX
Math 126
Tue 29 May 2012, 2:00pm-3:30pm

Abstract


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UBC
Wed 30 May 2012, 11:30am
Algebraic Groups and Related Structures
Math 126
A second word on Grothendieck topologies
Math 126
Wed 30 May 2012, 11:30am-1:00pm

Abstract

 TBA
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Daniel Valesin
UBC
Thu 31 May 2012, 2:00pm
Symbolic Dynamics and Ergodic Theory Seminar
Math 126
Thermodynamic Formalism X (Two phase transitions for the Gibbs states of the Ising model on trees )
Math 126
Thu 31 May 2012, 2:00pm-3:30pm

Abstract



We will start with a quick exposition of the random cluster representation of the Ising model on general graphs and see that this representation has a particularly simple form on trees. Relying on this, we will then study two phase transitions for the Ising model on trees (as the inverse temperature increases). The first one is the change from a unique Gibbs state to multiple Gibbs states. In the second one, the Gibbs state obtained from free boundary conditions changes from being extremal to non-extremal. The latter transition is related to the reconstruction problem in information networks. The talk will be partly based on the paper "Broadcasting on Trees and the Ising Model", by Evans, Kenyon, Peres and Schulman.
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