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Events - 2013

Tuesday, August 13, 2013 — 1:00 PM EDT

Alejandra Vicente-Colmenares

“The geometry of Yang-Mills fields, Part 08”

Throughout the spring 2013 term, we will (as a group) be reading through and lecturing on ”The Geometry of Yang-Mills Fields” by Sir Michael Atiyah. All are welcome to attend.

Tuesday, August 6, 2013 — 4:30 PM EDT

Omar Leon Sanchez, Department of Pure Mathematics and Natalie Mullin, Combinatorics Optimization

“Quantum Walks on Cycles and Algebraic Solutions”

Tuesday, August 6, 2013 — 3:00 PM EDT

Rahim Moosa, Pure Mathematics, University of Waterloo

"Dp-minimality (NIP XXI)"

We take a break from NIP to talk about dp-minimality. I will use a 2011 paper by Dolich, Goodrick, and Lippel.

Tuesday, August 6, 2013 — 1:00 PM EDT

Zhiyou Wu, Pure Mathematics, University of Waterloo

"Introduction to Hodge structures"

Hodge structure is an abstract notion modeled on the Hodge decomposition of cohomology groups of compact Kähler manifolds. We will introduce the basic notion of Hodge structure and see its relation with geometric objects such as abelian varieties and Riemann surfaces. If time permits we will discuss variation of Hodge structure, which is an important tool in complex algebraic geometry.

Tuesday, August 6, 2013 — 1:00 PM EDT

David Pazmino Pullas, Pure Mathematics, University of Waterloo

"A conjecture on 2-complexes"

This talk will be a very brief summary of the work done up to date on a question posted by J.H.C. Whitehead in 1941. We will go through the statement of the conjecture, and review some classical results. Finally, we will use an algebraic characterization of 2-complexes to understand one of the approaches taken to solve the problem.

Friday, August 2, 2013 — 3:30 PM EDT

David Farahany, Department of Pure Mathematics, University of Waterloo

“Problems with inverting the Fourier transform”

Friday, August 2, 2013 — 2:30 PM EDT

Joseph Miller, University of Wisconsin - Madison

"The degrees of relative provability"

Mingzhong Cai recently introduced the degrees of provability to
compare the proof-theoretic strength of statements asserting the
totality of computable functions. They can also be viewed as the
Lindenbaum algebra of true $\Pi^0_2$ statements in first-order
arithmetic. We investigate the structure of the degrees of

Thursday, August 1, 2013 — 2:00 PM EDT

Carrie Knoll, Pure Math Department, University of Waterloo

"Complexity of classes of structures"

The main theme of this thesis is classifying classes of structures relative to various measurements. We will briefly discuss the notion of computable dimension, while the breadth of the paper will focus on calculating the Turing ordinal and the back-and-forth ordinal of various theories, along with an exploration of how these two ordinals are related in general.

Tuesday, July 30, 2013 — 3:00 PM EDT

Omar Leon Sanchez, Department of Pure Mathematics, University of Waterloo

“NIP Theories XX” 

We will see why C-minimal theories are dp-mininal, and hence conclude that the theory ACVF is NIP. We will also see why ACFA is ”not” NIP.

Tuesday, July 30, 2013 — 2:30 PM EDT

Songhao Li, University of Toronto

“Elementary modification of Lie algebroids and the blow-up construction of Lie groupoids”

Tuesday, July 30, 2013 — 1:00 PM EDT

Travis Li, University of Toronto

“Introduction to Lie groupoids and Lie algebroids”

Monday, July 29, 2013 — 11:30 AM EDT

Chao Lin, Department of Pure Math, University of Waterloo

“Freiman’s Theorem - Part II”

Friday, July 26, 2013 — 3:30 PM EDT

Hun Hee Lee, Seoul National University

"Operator amenability of the $L^1$-algebra of a compact quantum group"

We consider the question of operator amenability of the $L^1$-algebra of a compact quantum group. In order to answer the question we instead look at a related concept of operator biflatness. The final result says for a
compact quantum group $G$, $L^1(G)$ is operator amenable if and only if $G$ is co-amenable and of Kac type, which excludes examples like

Tuesday, July 23, 2013 — 3:00 PM EDT

Omar Leon Sanchez, Department of Pure Mathematics, University of Waterloo

Title: NIP XIX

We will continue with the proof that the theory of algebraically closed valued fields has NIP. In the way we will talk about strongly dependent theories and dp-minimality.

Tuesday, July 23, 2013 — 1:00 PM EDT

Talk #1: "The Lefschetz Theorem on (1,1) Classes" (Zhiyou Wu)

We will discuss and give a proof of a special case of the Hodge conjecture: that for a smooth projective manifold, every (1,1) cohomology class is analytic. We will require some results from Kähler geometry, such as the Hodge-Dolbeault decomposition, which will be stated and their proofs sketched. If time permits we will make further remarks about the general Hodge conjecture.

Monday, July 22, 2013 — 11:30 AM EDT

Chao Lin, Department of Pure Mathematics, University of Waterloo

"Freiman's Theorem - Part I"

For a set of numbers $A$, let the sum-set $A+A$ denote

Friday, July 19, 2013 — 3:30 PM EDT

George Hutchinson, Department of Pure Math, University of Waterloo

“Almost Commuting Matrices and Lin’s Theorem”

Thursday, July 18, 2013 — 3:30 PM EDT

Matthew B. Young, Stony Brook University

“Representations of Hall algebras and some applications”

Tuesday, July 16, 2013 — 3:00 PM EDT

Omar Leon, Sanchez Department of Pure Mathematics, University of Waterloo

“NIP Theories XVIII”

We will take a step aside from Chapter 4 of Simon’s note, and jump the appendix to see why the theory of algebraically closed valued fields is NIP. Also, I will talk on why the model companion of difference fields is not NIP.

Monday, July 15, 2013 — 11:30 PM EDT

J.C. Saunders, Department of Pure Math, University of Waterloo

"Sums of Digits in q-ary expansions Part 2"

Let sq(n) denote the sum of the digits of a number n in base q. For example, s2(n) represents the number of 1s in the binary expansion of n. In 1978, Kenneth B. Stolarsky showed that lim inf n!1 s2(n2) s2(n)
= 0 using bounds obtained from analytical methods. In the last presentation we showed that the ratio s2(n2) s2(n) can indeed hit every positive rational number. In this presentation, we show that the same is

Friday, July 12, 2013 — 3:30 PM EDT

Seminar has been cancelled due to sickness.

Thursday, July 11, 2013 — 2:30 PM EDT

Robert Garbary, Pure Mathematics University of Waterloo

“Quotient Spaces”

Suppose we have an algebraic group G acting algebraicly on a variety X, ie for each g ∈ G the associated map X → X is a morphism. A quotient of X by G is defined to be a variety Y and a morphism π : X → Y satisfying
(1) π−1(π(x)) = Gx for all x ∈ X.
(2) For any variety Z and G-invariant morphism X → Z, there is a unique factorization through Y.

Thursday, July 11, 2013 — 1:15 PM EDT

Michael Ng, Department of Pure Math, University of Waterloo

“Dimension partition of some Cantor sets”

Please note room and time.

Tuesday, July 9, 2013 — 3:00 PM EDT

Ruizhang Jin, Department of Pure Mathematics, University of Waterloo

“NIP Theories XVII”

We will continue on chapter 4 of the Pierre Simons notes. We will go further on mutually indiscernible sequences and start talking about DP-ranks.

Tuesday, July 9, 2013 — 1:00 PM EDT

Benoit Charbonneau

“The geometry of Yang-Mills fields, Part 08"

Throughout the spring 2013 term, we will (as a group) be reading through and lecturing on ”The Geometry of Yang-Mills Fields” by Sir Michael Atiyah. All are welcome to attend.

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