2016 F. V. ATKINSON TEACHING AWARD

We are extremely happy to announce this year’s winners of the Frederick V. Atkinson Teaching Awards for Post Doctoral Fellows:

• André Belotto da Silva
• Anton Izosimov

The prize honors outstanding teaching by post-doctoral fellows and other junior research faculty not on the tenure track.

The awards recipients will receive a monetary award and a certificate during our awards/graduation reception scheduled for Thursday, May 26 at 3:10 p.m. in the Math lounge.

Congratulations to André and Anton!

Departmental PhD Thesis Exam – Andrew Stewart

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

Tuesday, June 28, 2016
3:10 p.m.
BA6183

PhD Candidate:  Andrew Stewart
Co-Supervisors:  Balint Virag
Thesis title:

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Abstract:

A copy of the thesis can be found here:

Departmental PhD Thesis Exam – Michal Kotowski

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

Tuesday, June 28, 2016
1:10 p.m.
BA6183

PhD Candidate:  Michal Kotowski
Co-Supervisors:  Balint Virag
Thesis title:

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Abstract:

A copy of the thesis can be found here:

Departmental PhD Thesis Exam – Marcin Kotowski

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

Tuesday, June 28, 2016
11:10 a.m.
BA6183

PhD Candidate:  Marcin Kotowski
Co-Supervisors:  Balint Virag
Thesis title:

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Abstract:

A copy of the thesis can be found here:

2016 Course Instructors Teaching Excellence Award Winner

Congratulations to our graduate student, Peter Crooks, winner of the 2016 CI Teaching Excellence Award.

In 2015, the Teaching Assistants’ Training Program’s (TATP) Teaching Excellence Award launched the first-ever TATP award specifically for graduate student Course Instructors.  This is a university-wide award that “recognizes one graduate student whose outstanding work as a sole-responsibility Course Instructor shows evidence of educational leadership, meaningful contributions to course and curriculum development, and impact on student learning.”

Peter is co-supervised by Lisa Jeffrey and John Scherk and is working in the area of Lie Theory and Equivariant Geometry.  Peter is defending his thesis this Wednesday, May 4, 2016.

2016 Daniel B. DeLury Teaching Assistant Awards winners

We are happy to announce that this year’s winners of the Daniel B. DeLury Teaching Assistant Awards for graduate students in mathematics are:

• Tracey Balehowsky
• Beatriz Navarro Lameda
• Nikita Nikolaev
• Asif Zaman

The selection committee consisted of Mary Pugh, Abe Igelfeld and Peter Crooks.  Nominations were made by faculty members, course instructors, and undergraduate students.

The awards recipients will receive a monetary award and a certificate during our awards/graduation reception scheduled for Thursday, May 26 at 3:10 p.m. in the Math lounge.

Congratulations Tracey, Beatriz, Nikita and Asif!

Ida Bulat Teaching Award for Graduate Students

The Department of Mathematics invites nominations for the inaugural:

Ida Bulat Teaching Award

This prize honors outstanding teaching by graduate students.  It is named in memory of Ida Bulat, former Graduate Administrator in the Department of Mathematics at the University of Toronto.

Nominations can be submitted online through this link, no later than Friday, May 13, 2016:

http://blog.math.toronto.edu/forms/nomination-form-2016/

Departmental PhD Thesis Exam – Trefor Bazett

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

Wednesday, May 11, 2016
11:10 a.m.
BA6183

PhD Candidate:  Trefor Bazett
Co-Supervisors:  Lisa Jeffrey/Paul Selick
Thesis title: The equivariant K-theory of commuting 2-tuples in SU(2)

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Abstract:

In this thesis, we study the space of commuting n-tuples in SU(2), $Hom(\mathbb{Z}^n, SU(2))$. We describe this space geometrically via providing an explicit G-CW complex structure, an equivariant analog of familiar CW- complexes. For the n=2 case, this geometric description allows us to compute various cohomology theories of this space, in particular the G-equivariant K-Theory $K_G^*(Hom(\mathbb{Z}^2, SU(2)))$, both as an $R(SU(2))$-module and as an $R(SU(2))$-algebra. This space is of particular interest as $\phi^{-1}(e)$ in a quasi-Hamiltonian system $M\xrightarrow{\phi} G$ consisting of the G-space $SU(2)\times SU(2)$, together with a moment map $\phi$ given by the commutator map. Finite dimensional quasi-Hamiltonian spaces have a bijective correspondence with certain infinite dimensional Hamiltonian spaces, and we additionally compute relevant components of this larger picture in addition to $\phi^{-1}(e)=Hom(\mathbb{Z}^2, SU(2))$ for this example.

A copy of the thesis can be found here: TreforBazettThesis

Departmental PhD Thesis Exam – Jennifer Vaughan

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

Monday, May 9, 2016
11:10 a.m.
BA6183

PhD Candidate:  Jennifer Vaughan
Co-Supervisors:  Yael Karshon
Thesis title:  Quantomorphisms and Quantized Energy Levels for Metaplectic-c Quantization

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Abstract:

Metaplectic-c quantization was developed by Robinson and Rawnsley as an alternative to the classical Kostant-Souriau quantization procedure with half-form correction.  This thesis extends certain properties of Kostant-Souriau quantization to the metaplectic-c context.  We show that the Kostant-Souriau results are replicated or improved upon with metaplectic-c quantization.

We consider two topics:  quantomorphisms and quantized energy levels.  If a symplectic manifold admits a Kostant-Souriau prequantization circle bundle, then its Poisson algebra is realized as the space of infinitesimal quantomorphisms of that circle bundle.  We present a definition for a metaplectic-c quantomorphism, and prove that the space of infinitesimal metaplectic-c quantomorphisms exhibits all of the same properties that are seen in the Kostant-Souriau case.

Next, given a metaplectic-c prequantized symplectic manifold $(M,\omega)$ and a function $H\in C^\infty(M)$, we propose a condition under which $E$, a regular value of $H$, is a quantized energy level for the system $(M,\omega,H)$.  We prove that our definition is dynamically invariant:  if two functions on $M$ share a regular level set, then the quantization condition over that level set is identical for both functions.  We calculate the quantized energy levels for the $n$-dimensional harmonic oscillator and the hydrogen atom, and obtain the quantum mechanical predictions in both cases.  Lastly, we generalize the quantization condition to a level set of a family of Poisson-commuting functions, and show that in the special case of a completely integrable system, it reduces to a Bohr-Sommerfeld condition.

The draft to the thesis can be found here: Vaughan-Draft

Departmental PhD Thesis – Iva Halacheva

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

TBA
BA6183

PhD Candidate:  Iva Halacheva
Co-Supervisors:  Dror Bar-Natan, Joel Kamnitzer
Thesis title: