Courses: ongoing

Registration for this course is not currently available.

Discrete optimization focuses on developing efficient methods to determine the maximum or minimum value of a function over a finite (discrete) domain. This course will cover a wide range of topics in discrete optimization which may include linear programming, semi-definite programming, dynamic programming, matroids, combinatorial algorithms, duality, hardness reductions, among others. We will also see many interesting applications of tools from Discrete Optimization to problems in combinatorics and other areas of mathematics and computer science.

Course Webpage

This course will have an accompanying webpage

• https://extremalcombinatorics.com/optimization/

Materials related to the course, links and other updates will be posted to the course webpage as the course proceeds.

Class Schedule

• Monday, Thursday 1:00-2:20pm (PT)

Remote Access

Remote access for this course will be provided via zoom. This course will be taught from the UVic Multiaccess classroom HHB 110. The room is equipped with multiple cameras in the ceiling which can capture two blackboard areas and TV screens that can be used to show the Zoom gallery. A demonstration of this system can be seen in the instructor’s existing Extremal Combinatorics Network Wide Course playlist. Notes and other course related material will be made available on the instructor’s website (see e.g. notes for Extreemal Combinatorics).

Lectures will also be live-streamed on the instructors YouTube channel and also be available to view there asynchronously.

Availability

This course may be open to students from universities outside of the PIMS network, and those coming from industry/government.

Registration for this course is not currently available.

This course is an introduction to the theory of elliptic curves and modular forms at the graduate level. Elliptic curves will be introduced through both their classical analytic construction over the real and complex numbers and their algebraic realizations via normal forms over arbitrary fields. Moduli and monodromy considerations lead us to study the special role of the elliptic modular group SL(2,Z) and the crucial notions of modular functions and forms. Studying torsion points and level structure then motivates the extension to finite index subgroups and the theory of modular curves. Throughout the course, there will be an emphasis on hands-on explicit computations. Directed by the instructor, each student will complete a final project, presentation, and paper. Possible topics could include post-quantum elliptic curve cryptography, applications in string theory, geometry of elliptic modular surfaces, features of periods and Picard-Fuchs operators, etc.

Class Schedule

• Tuesday and Thursday, 16:00 - 17:20 MST

Remote Access

The course will be taught over Zoom using a tablet and shared screen. Lecture notes will be written out live on a tablet. There will also be pre-prepared slides on certain topics. The in-class lecture notes will be saved and distributed as .pdf files. There will be a course webpage to host all of these plus additional course materials and readings.

The format will be Zoom based, with videos on. Breakout rooms will be used periodically for small group work. Students will be encouraged to “raise hands” with questions at any time.

Availability

This course may be open to students from universities outside of the PIMS network, and those coming from industry/government.

Registration for this course is not currently available.

This graduate course is designed to provide graduate students with key concepts and practical applications in Biophysics, with an emphasis on the quantitative tools as they are used in current research. Biophysics is a highly interdisciplinary field—the researchers who attend the annual Biophysical Society meeting, for example, come from departments spanning all of the STEM disciplines. Nevertheless, they share a common interest to establish a quantitative understanding of living matter. Despite growing interest however, a gap remains in graduate training to prepare students to contribute effectively to this broad and rapidly evolving field. This course aims to address this gap by covering both foundational and advanced concepts and applications that are commonly used by practicing biophysicists today. The structure of the course will follow selected advanced material from Physical Biology of the Cell by Rob Phillips, Jane Kondev, Julie Theriot, and Hernan G. Garcia. Each topic will be introduced conceptually, developed mathematically, and explored through real biological case studies using both textbook material and current literature. Given student interest, the course may include interviews with leading biophysicists on their recent published work. Topics will include:

• Diffusion problems in biology
• Enzymatic reactions including ODEs, diffusion-limited reactions, and Michaelis-Menton reactions
• Statistical mechanics as it applies to Biology, including Gibbs free energy of biochemical reactions
• Liquid-liquid phase separation, and its role in the cell and in transcription
• Polymer physics; DNA looping, persistence length, polymer entropy
• Heterogeneous mixtures and osmotic pressure
• Quantitative analysis of genetic networks
• Expression distributions of transcription and translation
• Phase portrait analysis and stability/metastability of cellular states
• Genetics of enhancers – from a biophysical perspective
• Pattern formation including Turing patterns, symmetry breaking in an embryo
• Quantitative genomics (time permitting)

Class Schedule

• Wed, Fri 10am-11:30am (classes will begin Sept. 10)

Remote Access

Remote participation will be via zoom. Lectures will also be recorded and shared via UBC’s media capture system Panopto. Annotated notes on pre-distributed PDF slides are made during class using an iPad, recorded in real time, and uploaded to UBC’s Canvas server after class, along with links to the lecture recording.

Availability

This course may be open to students at universities outside of the PIMS network.

Grading

There will be no Final exam, instead there will be a final project. I’ve tentatively planned for an in-class midterm, but as a directed studies class, this may become a “take-home” midterm. For percentages, here is a tentative breakdown:

Homework (45%)

Homework due each Sunday at 11:59 pm.

Homework is assigned a week prior to the due date. I will allow late homework, however a 10% penalty per day after the due date is applied to late HW. There will be ~11 homework assignments. Assignments are roughly the same length; The points for each assignment will be weighted proportional to the number of problems in it.

Midterm (20%)

The midterm will take place on evening of Nov 13 or Nov 14 at 6 pm.

The content cut-off for the material will be up and including the Friday before midterm break (Nov 7) and the format will be discussed in class in advance. Email me by Friday Sept 12 if you have a conflict (steve@phas.ubc.ca). The in-class midterm may be replaced with a take-home midterm. |

Final Project (20%)

Date and time the final project is due will be announced, but it will be some time during the Dec exam period. We will discuss how to best design these projects to be most beneficial to everyone.

Guest speaker interviews and Lab Tutorial (15%)

I am thinking of including interviews of postdocs or professors, as I have done in the past. If we do this, we will read an assigned publication by a guest scientist or their lead first-author student/PDF, and we will then interview that scientist/student on the paper. Both general and specific questions may be asked during each interview. However, technical questions specific to the paper are essential for credit. The number of interviews we have is TBD.

One of your planned assignments will also be to complete a lab tutorial involving some more open-ended questions about experimental observations, which will be described further in Module 7 of the course.

Textbook

The textbook for Physics 305 is Physical Biology of the Cell (2nd edition), by Rob Phillips, Jane Kondev, Julie Theriot, and Hernan Garcia. It is available from multiple resources including Amazon as either a paperback or eTextbook. Downloadable resources for the text are here. We will also use material from select journal sources.

Registration for this course is not currently available.

This course is a bridge into the machine learning literature for graduate students in mathematics. Compared to existing course offerings in our neighbouring departments (mainly https://www.cs.ubc.ca/~dsuth/532D/23w1 (https://www.cs.ubc.ca/~dsuth/532D/23w1)) we will assume that you know somewhat more analysis, but prior coding experience will not be required. Briefly, the learning objectives are:

• understand the different “learning paradigms” considered in ML (supervised learning, unsupervised learning, reinforcement learning, etc.) and their relation with existing statistical theory
• be comfortable with mathematical tools (eg. kernel methods) which appear commonly in the ML literature but are not well known among pure mathematicians
• see some natural connections between ML theory and: optimization/calculus of variations, measure theory, PDE, etc
• gain fluency reading ML papers (which can be less trustworthy than pure math papers)
• start to think about how to bring your area of mathematical expertise to bear on ML problems.

Outline:

• Unit 0: (~1 week) What is machine learning?
• Unit 1: (~4 weeks) Supervised learning: The statistical learning theory framework. Inference in high dimension. Falsibiability of models and measures of model complexity. Regression and classification. Kernel methods. Learning with neural networks. Double-descent and failure of Ockham’s razor.
• Unit 2: (~3 weeks) Unsupervised learning: Clustering and dimensionality reduction. Manifold hypothesis. Geometric graph methods. Inferring probability distributions: density estimation, sampling, generative models.
• Unit 3: (~4 weeks) Reinforcement learning: Exploration-exploitation tradeoff. Sequential decision problems. Markov decision processes and connections with control theory. Efficient exploration for bandit problems and small-scale games. Complexity notions and learnability for large scale games.

Main references: for textbook references we will use a couple chapters from each.

• Unit 0: Vapnik, “The nature of statistical learning theory”.
• Unit 1: Wainwright, “High-dimensional statistics”. Bach, “Learning theory from first principles”.
• Unit 2: There is no good textbook for unsupervised learning that I am aware of. I have course notes. We will also look at some classic research papers, for example for geometric graph methods we will read “Laplacian eigenmaps for dimensionality reduction and data representation” by Belkin and Niyogi.
• Unit 3: Foster and Rakhlin, RL theory notes: https://arxiv.org/abs/2312.16730

Class Schedule

• TBA

Remote Access

Remote access to this course will be via zoom. The delivery mechanism will be either blackboard or via tablet depending on available rooms. A PDF textbook and/or research article readings will be distributed in advance of each class.

Availability

This course may be open to students from universities outside of the PIMS network.

Registration for this course is not currently available.

In this course we are learning to build and analyse nonlinear partial differential equation models. The focus of the course will be models of ecological systems, but the techniques learned apply broadly across application areas. We learn a wide variety of analytic, graphic, and simplification techniques which elucidate the behaviour of these mathematical models, whether or not a closed-form solution is available. By the end of the class, the students will be able to competently read and follow a research paper presenting and analysing a differential equation model from a wide variety of application areas. Broadly, the topics that we cover are applications of ecological applications of travelling waves, disease models, and pattern formation in reaction-diffusion and reaction-diffusion-chemotaxis models.

Class Schedule

TBA

Remote Access

Lectures will be livestreamed via zoom. The lecturer will be writing on a whiteboard interspersed with pdf presentations. Lecture notes will be posted on Canvas.

Availability

This course may be open to students from universities outside of the PIMS network.