Colloquium: Yuriy Zinchenko (U. Calgary) @ Keller 401
May 3 @ 3:00 pm – 4:00 pm

Dose-volume requirements modeling for radiotherapy optimization

Radiation therapy is an important modality in cancer treatment. To find a good treatment plan, optimization models
and methods are typically used, while dose-volume requirements play an important role in plan’s quality evaluation.
We compare four different optimization approaches to incorporate the so-called dose-volume constraints into the
fluence map optimization problem for intensity modulated radiotherapy. Namely, we investigate (1) conventional
emph{Mixed Integer Programming} (MIP) approach, (2) emph{Linear Programming} (LP) approach to partial volume
constraints, (3) emph{Constrained Convex Moment} (CCM) approach, and (4) emph{Unconstrained Convex Moment
Penalty} (UCMP) approach. The performance of the respective optimization models is assessed using anonymized data
corresponding to eight previously treated prostate cancer patients. Several benchmarks are compared, with the goal
to evaluate the relative effectiveness of each method to quickly generate a good initial plan, with emphasis on
conformity to DVH-type constraints, suitable for further, possibly manual, improvement.

Dr. Zinchenko received his PhD from Cornell University on 2005 under supervision of Prof. James Renegar.
From 2005 to 2008 he held a PDF position at the Advanced Optimization Lab at McMaster University, working
with Prof. Tamas Terlaky and Prof. Antone Deza, and spent portion of his fellowship with radiation oncology group
at the Princess Margaret Hospital in Toronto. Currently, Yuriy is an Associate Professor of Mathematics & Stat at the
University of Calgary.
Dr. Zinchenko’s primary research interest lies in convex optimization, and particularly, the curvature of the central path for
interior-point methods, and applications. Yuriy’s work on optimal radiotherapy design was recognized by 2008 MITACS
Award for Best Novel Use of Mathematics in Technology Transfer, and in 2012-2015 he served as one of the PIs for
PIMS Collaborative Research Group grant on optimization.

MA defense: Sean Sanford
May 4 @ 9:30 am – 10:30 am

Smooth Actions of Compact Lie Groups on $S^2$ are Smoothly Equivalent to Linear Actions:

Link to Master’s project


Mathematicians have been interested in group actions on spheres since before the algebraic description of a group was defined. The rotational and reflective symmetries of the circle and of S^2 were naturally among the first to be considered. When we restrict attention to a compact topological group, there is a classic theorem of Kerekjártó to the effect that for S^2 , these are essentially the only actions:

Theorem 1 (Kerekjártó, [3]). Every continuous, effective action of a compact topological group G on S^2 is topologically conjugate to a linear action (to the standard action of a subgroup of O(3) on S^2 as a subset of R^3 ).

Thus in the topological category, in order to understand all effective actions of compact groups on S^2 , it is enough to understand the subgroups G ≤ O(3) and their actions via matrix multiplication on S^2 ⊆ R^3 (so called linear actions).

The goal of this paper is to extend this result to the smooth category. In other words, we show that every smooth, effective action of a compact Lie group, on S^2 is smoothly conjugate (i.e. conjugate through a diffeomorphism) to a linear action.

The main theorem of the paper is helpful for studying the topology of the space of actions of compact Lie groups on S^2 and we present a corollary as an example of this. We also explicitly determine all compact subgroups of O(3) up to conjugacy within O(3), and use this information to construct explicit G-CW decompositions for preferred representatives of each of these conjugacy classes. The G-CW decompositions are useful in other areas for example in the classification of G-equivariant vector bundles over S^2, and in determining whether such bundles have algebraic models.

Logic Seminar: David Webb
May 5 @ 1:00 pm – May 5 @ 2:00 pm
PhD Defense – Ka Lun Wong @ TDA
Jul 11 @ 3:00 pm – 4:00 pm
2019 AMS Sectional Meeting
Mar 29 – Mar 31 all-day

University of Hawaiʻi at Mānoa