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For a finite set X, a family F of subsets of X is said to be increasing if any set A that contains B in F is also in F. The p-biased product measure of F increases as p increases from 0 to 1, and often exhibits a drastic change around a specific value, which is called a "threshold." Thresholds of increasing families have been of great historical interest and a central focus of the study of random discrete structures (e.g. random graphs and hypergraphs), with estimation of thresholds for specific properties the subject of some of the most challenging work in the area. In 2006, Jeff Kahn and Gil Kalai conjectured that a natural (and often easy to calculate) lower bound q(F) (which we refer to as the “expectation-threshold”) for the threshold is in fact never far from its actual value. A positive answer to this conjecture enables one to narrow down the location of thresholds for any increasing properties in a tiny window. In particular, this easily implies several previously very difficult results in probabilistic combinatorics such as thresholds for perfect hypergraph matchings (Johansson–Kahn–Vu) and bounded-degree spanning trees (Montgomery). I will present recent progress on this topic in the first talk, and discuss more details about proof techniques in the second talk. Based on joint work with Keith Frankston, Jeff Kahn, Bhargav Narayanan, and Huy Tuan Pham.

For a finite set X, a family F of subsets of X is said to be increasing if any set A that contains B in F is also in F. The p-biased product measure of F increases as p increases from 0 to 1, and often exhibits a drastic change around a specific value, which is called a "threshold." Thresholds of increasing families have been of great historical interest and a central focus of the study of random discrete structures (e.g. random graphs and hypergraphs), with estimation of thresholds for specific properties the subject of some of the most challenging work in the area. In 2006, Jeff Kahn and Gil Kalai conjectured that a natural (and often easy to calculate) lower bound q(F) (which we refer to as the “expectation-threshold”) for the threshold is in fact never far from its actual value. A positive answer to this conjecture enables one to narrow down the location of thresholds for any increasing properties in a tiny window. In particular, this easily implies several previously very difficult results in probabilistic combinatorics such as thresholds for perfect hypergraph matchings (Johansson–Kahn–Vu) and bounded-degree spanning trees (Montgomery). I will present recent progress on this topic in the first talk, and discuss more details about proof techniques in the second talk. Based on joint work with Keith Frankston, Jeff Kahn, Bhargav Narayanan, and Huy Tuan Pham.

Description:
  The classical obstacle problem consists of finding the equilibrium position of an elastic membrane whose boundary is held fixed and which is constrained to lie above a given obstacle. By classical results of Caffarelli, the free boundary is smooth outside a set of singular points. However, explicit examples show that the singular set could be, in general, as large as the regular set. This talk aims to introduce this beautiful problem and describe some classical and recent results on the regularity of the free boundary.

Speaker Biography:
Alessio Figalli is a leading figure in the areas of Optimal Transport, partial differential equations and the calculus of variations. He received his Ph.D. from the Scuola Normale Superiore di Pisa and the Ecole Normale Superieur de Lyon and has held positions in Paris and Austin, Texas. He is currently a Professor at ETH Zurich. His work has been recognized with many awards including the Prize of the European Mathematical Society in 2012 and the Fields Medal in 2018.

Time:
All network wide colloquia take place at 1:30pm Pacific Time with a few exceptions.

Registration:
To attend this event please register here to receive the meeting link. Talks will be recorded and posted on the PIMS resource page www.mathtube.org.

Coffee and muffins at 2:15pm

Abstract: How many lines are spanned by a set of planar points?. If the points are collinear, then the answer is clearly "one". If they are not collinear, however, several different answers exist when sets are finite and "how many" is measured by cardinality. I will discuss a bit of the history of this problem and present a recent extension to the discretized and continuum settings, obtained in collaboration with T. Orponen and H. Wang. No specialized background will be assumed.

Pablo is a leader in the area of fractal geometry. He is a recent speaker at the International Congress of Mathematicians; and a Canada Research Chair at UBC.

Note that you need to register in advance at this web site.

The past twenty-five years have heralded an unparalleled increase in understanding of cancer. At the same time, mathematical modelling has emerged as a natural tool for unravelling the complex processes that contribute to the initiation and progression of tumours, for testing hypotheses about experimental and clinical observations, and assisting with the development of new approaches for improving its treatment. In this talk I will reflect on how increased access to experimental data is stimulating the application of new theoretical approaches for studying tumour growth. I will focus on two case studies which illustrate how mathematical approaches can be used to characterise and quantify tumour vascular networks, and to understand how microstructural features of these networks affect tumour blood flow.

This event is part of the PIMS sponsored Seminar Series: Mathematics of Ethical Decision-making Systems

Download Poster.

Speakers:

• Midori Ogasawara, Assistant Professor, UVic Sociology
• Patricia Cochran, Associate Professor, UVic Law
• Freya Kodar, Associate Professor, UVic Law
• Jentery Sayers, Associate Professor, UVic English

AGENDA:

• 3:00 pm Dr. Midori Ogasawara will speak on the social consequences of surveillance and data collection.
• 3:30 pm Break for refreshments
• 4:00 pm Dr. Patricia Cochran and Dr. Freya Kodar
  Title: Technology, access to justice and narratives of law in an unequal society In this presentation, we will share some information about our ongoing research collaborations about the relationship between access to justice and technologically-mediated decision-making (including algorithmic credit-scoring and the online Civil Resolution Tribunal). We will discuss some of the critical questions we think require interdisciplinary attention given the growing significance of technology in legal processes, and the challenges that such processes pose for important legal ideas such as equality.
• 4:30 pm Dr. Jentery Sayers
  Title: Modelling Games as Activity Systems to Evaluate the Generative Contradictions between Play and Work I’ll talk about the articulation of genre studies with cultural-historical activity theory to consider conflicting motives in video games. I’m hoping to focus on contradictions related to labour (e.g., between dev teams and players; between types of players), metagaming (e.g., between social norms and player activities that may be considered cheating), and genre (between storytelling and mechanics, or “ludonarrative dissonance”). I’ll ground the talk in the model of activity theory rather than the particulars of these contradictions and conflicts.
• 5:00 -5:30 pm Panel Discussion

**For those unable to attend in person, there will be a virtual component - e-mail Kristina at pims@uvic.ca for this ‘virtual attendance’ information.**

Talk is at 3:30 pm.

Reception is at 4:30 pm.

Download poster (PDF).

Abstract: Prediction systems face exogenous and endogenous distribution shift -- the world constantly changes, and the predictions the system makes change the environment in which it operates. For example, a music recommender observes exogeneous changes in the user distribution as different communities have increased access to high speed internet. If users under the age of 18 enjoy their recommendations, the proportion of the user base comprised of those under 18 may endogeneously increase. Most of the study of endogenous shifts has focused on the single decision-maker setting, where there is one learner that users either choose to use or not. In this talk, I'll describe several settings where user preferences may cause changes in distributions over the life of an ML system, and how these changes will affect the long-term performance of such systems. Joint work with Sarah Dean, Mihaela Curmei, Maryam Fazhel and Lillian Ratliff.

Bio: Jamie Morgenstern is an assistant professor in the Paul G. Allen School of Computer Science and Engineering at the University of Washington. She was previously an assistant professor in the School of Computer Science at Georgia Tech. Prior to starting as faculty, she was fortunate to be hosted by Michael Kearns, Aaron Roth, and Rakesh Vohra as a Warren Center fellow at the University of Pennsylvania. She completed her PhD working with Avrim Blum at Carnegie Mellon University. She studies the social impact of machine learning and the impact of social behavior on ML's guarantees. How should machine learning be made robust to behavior of the people generating training or test data for it? How should ensure that the models we design do not exacerbate inequalities already present in society?

For those unable to attend this talk in person, we have a Zoom alternative. For the Zoom meeting ID/Passcode, please send an email to pims@uvic.ca. Thank you

Join us for this talk in the Seminar Series: Mathematics of Ethical Decision-making Systems

Talk at 3:30 PM
Reception at 4:30 PM

Fairness in machine learning classification has been a topic of great interest given the increasing use of such classifiers in critical settings.

There are many possible definitions of fairness and many potential sources of unfairness. Given this complex landscape, most research has focused on studying single classifiers in isolation.

In reality an individual is subjected to a network of classifiers: for example, one is classified at each stage of life (school, college, employment to name a few), and one may also be classified in parallel by many classifiers (such as when seeking college admissions). In addition, individuals may modify their behavior based on their knowledge of the classifier, leading to equilibrium phenomena. Another feedback effect is that the result of the classifier may affect the features of an individual (or of the next generation) for future classifications.

In this talk we present work that takes the first steps in exploring questions of fairness in networks of classifiers and in systems with feedback. Given the inherent complexity of the analysis, our models are very stylized, but it is our belief that some of the qualitative conclusions apply to real-world situations.

***For those unable to attend this talk in person, we have a Zoom alternative. For the Zoom meeting ID/Passcode, please send an email to pims@uvic.ca. Thank you ***

Download Poster (PDF)