Graduate Blog

Everyone welcome.  Refreshments will be served in the Math Lounge before the exam.

Monday, May 28, 2012, 11:10 a.m., in BA 6183, 40 St. George Street

PhD Candidate:  Henning Petzka

PhD Advisor:  George A. Elliott

Thesis Title:  Stably non-stable C*-algebras with no bounded trace
               (www.math.toronto.edu/hpetzka/thesis)

Thesis Abstract:

A well-known theorem of Blackadar and Handelman states that every unital stably
finite C*-algebra has a bounded quasitrace. Rather strong generalizations of
stable finiteness to the non-unital case can be obtained by either requiring
the multiplier algebra to be stably finite, or alternatively requiring it to be
at least stably not properly infinite. My thesis deals with the question whether
the Blackadar-Handelman result can be extended to the non-unital case with
respect to these generalizations of stably finiteness.

For suitably well-behaved C*-algebras there is a positive result, but none of
the non-unital versions holds in full generality. Two examples of C*-algebras
are constructed. The first one is a non-unital, stably commutative C*-algebra
A that contradicts the weakest possible generalization of the Blackadar-Handelman
theorem: The multiplier algebras of all matrix algebras over A are finite,
while A has no bounded quasitrace. The second example is a non-unital, simple
C*-algebra B that is stably non-stable, i.e. no matrix algebra over B is a stable
C*-algebra. In fact, the multiplier algebras over all matrix algebras of this
C*-algebra are not properly infinite. Moreover, the C*-algebra B has no bounded
quasitrace and therefore gives a simple counterexample to a possible
generalization of the Blackadar-Handelman theorem.

Everyone welcome.  Refreshments will be served in the Math Lounge before the exam.

Tuesday, May 29, 2012, 10:10 a.m., in BA 6183, 40 St. George Street

PhD Candidate: Nevena Francetic

PhD Advisor: Eric Mendelsohn

Thesis Title: Covering Arrays with Row Limit
(http://www.math.toronto.edu/nfrancet/mojaTeza.pdf)

Thesis Abstract:

Covering arrays with row limit, CARLs for short, are a generalization of group divisible designs and covering arrays. Similarly to their predecessor, CARLs have a natural application as combinatorial models for interaction test suites. A CARL(N;t,k,v: w), is an N×k array with some empty cells. A component, which is represented by a column, takes values from a v-set called the alphabet. In each row, there are exactly w non-empty cells, that is the corresponding components have an assigned value from the alphabet. The parameter w is called the row limit. Moreover, any N×t subarray contains every of v^t distinct t-tuples of alphabet symbols at least once.

This thesis is concerned with the bounds on the size and constructions of CARLs when the row limit w(k) is a positive integer valued function of the number of columns, k. Here we give a lower bound, and probabilistic and algorithmic upper bounds for any CARL. Further, we find improvements on the upper bounds when w(k)lnw(k) = o(k) and when w(k) is a constant function. We also determine the asymptotic size of CARLs when w(k) = Θ(k) and when w(k) is constant.

Next, we study constructions of CARLs. We provide two combinatorial constructions of CARLs, which we apply to construct families of CARLs with w(k) = ck, where c < 1.  Also, we construct optimal CARLs when t = 2 and w = 4, and prove that there exists a constant δ, such that for any v and k ≥ 4, an optimal CARL(2,k,v: 4) differs from the lower bound by at most δ rows, with some possible exceptions.

Finally, we define a packing array with row limit, PARL(N;t,k,v: w), the same as a CARL(N;t,k,v: w) with the difference that any t-tuple is contained at most once in any N × t subarray. We find that when w(k) is a constant function, the results on the asymptotic size of CARLs imply the results on the asymptotic size of PARLs. Also, when t = 2, we consider a transformation of optimal CARLs with row limit w = 3 to optimal PARLs with w = 3.

———- Forwarded message ———-
From: 9th Advanced Course in Operator Theory and Complex Analysis
Date: Friday, May 11, 2012
Subject: Second announcement: Ninth Advanced Course in Operator Theory and Complex Analysis, Sevilla June 2012
To: colliand@math.toronto.edu

Dear colleagues,

We have the pleasure to inform you that the Ninth edition of the
Advanced Course in Operator Theory and Complex Analysis will take
place again in Sevilla (Spain) from the 12th to the 14th of June
2012. The list of the main invited speakers will be the following:

Wolfang Arendt
Universität Ulm
(Germany)

Joseph A. Ball
Virginia Tech
(USA)

Isabelle Chalendar
Université Lyon-1
(France)

Sjoerd Verduyn Lunel
Universiteit Leiden
(Netherlands)

Armen G. Sergeev
Steklov  Mathematical Institute of  Moscow
(Russia)

In addition, there will be four more invited lectures delivered by

Evgeny Abakumov
Université Paris-Est Marne-la-Vallée
(France)

Håkan Hedenmalm
KTH
(Sweeden)

Jonathan R. Partington
Leeds University
(United Kingdom)

Alexei Poltoratski
Texas A&M University
(USA)

Apart of attending the course, participants will also have the
opportunity to deliver contributed talks.

Further information about the course can be found at

http://congreso.us.es/ceacyto/2012

Information about each one of the previous editions is available at
the corresponding webpages

http://congreso.us.es/ceacyto/2004
,
http://congreso.us.es/ceacyto/2005
,
http://congreso.us.es/ceacyto/2006
,
http://congreso.us.es/ceacyto/2007
,
http://congreso.us.es/ceacyto/2008
,
http://congreso.us.es/ceacyto/2009
,
http://congreso.us.es/ceacyto/2010

and

http://congreso.us.es/ceacyto/2011

Please feel free to pass on this information to any colleague who
might be interested in our meeting.

Sincerely,
The organizers.

Everyone welcome. Refreshments will be served in the Math Lounge before the exam.

Friday, May 18, 2012, 2:10 p.m., in BA 6183, 40 St. George Street

PhD Candidate: Karene Chu

PhD Advisor: Dror Bar-Natan

Thesis Title: Flat Virtual Pure Tangles (http://www.math.toronto.edu/karene/Thesis120509.pdf)

Thesis Abstract:

Virtual knot theory, introduced by Kauffman, is a generalization of classical knot theory which interests us because its finite-type invariant theory is potentially a topological interpretation of Etingof and Kazhdan’s theory of quantization of Lie bialgebras. Classical knots inject into virtual knots, and flat virtual knots is the quotient of virtual knots which equates the real positive and negative crossings, and in this sense is complementary to classical knot theory within virtual knot theory.

We classify flat virtual tangles with no closed components and give bases for its “infinitesimal” algebras. As a corollary, we also obtain a classification of free virtual tangles with no closed components. The classification of the former can be used as an invariant on virtual pure tangles. In a subsequent paper, we will show that the infinitesimal algebras are indeed the target spaces of any universal finite-type invariants on the respective variants of flat virtual tangles.

Everyone welcome. Refreshments will be served in the Math Lounge before the exam.

Monday, May 14, 2012, 2:10 p.m., in BA 6183, 40 St. George Street

PhD Candidate:  Kam-Fai Tam

PhD Advisor:    James Arthur

Thesis Title:  Transfer relations in essentially tame local Langlands correspondence
(http://www.math.toronto.edu/graduate/Tam-thesis.pdf)

Thesis Abstract:

Let $F$ be a non-Archimedean local field and $G$ be the general
linear group $GL_n$ over $F$.  Bushnell and Henniart described the
essentially tame local Langlands correspondence of $G(F)$ using
rectifiers, which are certain characters defined on tamely ramified
elliptic maximal tori of $G(F)$. They obtained such result by studying
the automorphic induction character formula. We relate this formula
with the spectral transfer character formula, based on the theory of
twisted endoscopy of Kottwitz, Langlands and Shelstad. The two
main results in this article are

(i) to show that the automorphic induction character formula is equal
to the spectral transfer character formula under the same
Whittaker normalization and

(ii) to express the essentially tame local Langlands correspondence
using the admissible embeddings constructed by Langlands-Shelstad
$\chi$-data, and to express the rectifiers of Bushnell-Henniart
by certain endoscopic transfer factors.

Two reminders:

If you like to attend the Math Graduate Student Career Event

http://www.math.toronto.edu/cms/assets/MathFiles/Home/Files/Grad-career.pdf

this Wednesday, May 2nd, please RSVP by noon this Monday at

http://www.doodle.com/hp7hnzux2unuux95

We will need to know how much food to order.

The deadline to submit your reading and/or research course forms
for master’s projects and summer reading courses is MONDAY, MAY 7th.
The completed forms come to me. Blank forms are available in the
mailroom.

I will be away from the office from Monday, May 14 and will return
on Monday, May 28. If you need any confirmation letters from me, please request
them before I leave. While I am away, Jemima in the main office will
be able to assist you.

Thanks!

Ida

On behalf of the organizing committee of the Ottawa Mathematics Conference
(OMC), I’d like to ask you to encourage your students to give a talk at
this year’s event. The OMC is a two-day conference designed specifically
for graduate students, postdocs, and talented undergraduates to showcase
their research in any field of mathematics. It is a great opportunity not
only to interact with fellow mathematicians, but also to gain experience
in giving talks and sharing one’s work.

The OMC will take place at the University of Ottawa from May 18-19, 2012.
Talks need only be 25 minutes in length, and slots are still available!
Much more information (including information about registration) can be
found on our website: www.omc2012.com.

If you have a student who has research to share, please encourage him or
her to register! And if you have have any questions, please don’t hesitate
to send me an e-mail at ckari099@uOttawa.ca.

Sincerely,

Camelia Karimianpour

PhD student

Department of Mathematics and Statistics

University of Ottawa

585 King Edward
Ottawa, ON

K1N 6N5

Email: ckari099@uottawa.ca

Everyone is welcome. There will be refreshments served in the Math Lounge before the exam.

DEPARTMENTAL PHD THESIS EXAM

Monday, April 30, 2012, 2:10 p.m., in BA 6183, 40 St. George St.

PhD Candidate: Artem Dudko

PhD Advisor: Michael Yampolsky

Thesis Title: Dynamics of holomorphic maps: Resurgence of Fatou coordinates, and Poly-time computability of Julia sets. (http://www.math.toronto.edu/graduate/Dudko-thesis.pdf)

Thesis Abstract:

My thesis consists of two parts. The first part concerns the dynamics of germs with a simple parabolic fixed point at the origin
\[F(w)=w+w^2+O(w^3).\] The second part is on Computability of Julia sets. In this talk I will present the results of the first part of the thesis.

Let $F$ be a germ with a simple parabolic fixed point at the origin. It is convenient to apply the change of coordinates $z=-1/w$ and consider the germ at infinity
\[f(z)=-1/F(-1/z)=z+1+O(z^{-1}).\] The dynamics of a germ $f$ can be described using Fatou coordinates. The Fatou coordinates are analytic solutions of
the equation \[\phi(f(z))=\phi(z)+1.\] This equation has a formal solution \[\tilde{\phi}(z)={\rm const}+z+A\log z+\sum_{j=1}^\infty b_jz^{-j},\] where $\sum b_jz^{-j}$ is a divergent power series. Using Écalle’s Resurgence Theory I show that $\tilde{\phi}$ can be interpreted as the asymptotic expansion of the Fatou coordinates at infinity. Moreover, the Fatou coordinates can be obtained from $\tilde \phi$ using Borel-Laplace summation. J. Écalle and S. Voronin independently constructed a complete set of invariants of analytic conjugacy classes of germs
with a parabolic fixed point. I give a new proof of validity of Écalle’s construction.

Hello,

My name is Aadita Chaudhury and I am the outgoing Co-President of LGBTQ and Allies in Engineering (LGBTQAE), a student organization in the Faculty of Applied Science & Engineering. Since our inception in September 2011, we have been committed to creating a safe and accepting space for engineering students, staff and faculty members regardless of gender identity, gender expression or sexual orientation through social, professional and leadership development events. For the upcoming year, we are aiming to open our membership to all students in the Science, Technology, Engineering and Mathematics (STEM)-related fields since we feel that there is a need for discourse and association relating to LGBTQ issues which focuses on the unique needs of the people in these fields. We are interested in reaching out to your student body to join our organization as general members or to run for executive positions for the next academic year. I would like to please request you to pass on this information to your student body so that interested parties can directly get in touch with us. If you require more information about our activities and events, please feel free to get in touch with me at aadita.chaudhury@utoronto.ca. I am also available to meet with you in person to discuss further details. I look forward to hearing back from you soon regarding this.

Sincerely,

Aadita Chaudhury

Co-President, LGBTQ and Allies in Engineering

Faculty of Applied Science & Engineering

University of Toronto