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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.

Register via Zoom to receive the link for this event and the rest of the series.

ABSTRACT: Stochastic parameterizations (SMCM) are continuously providing promising simulations of unresolved atmospheric processes for global climate models (GCMs). One of the features of earlier SMCM is to mimic the life cycle of the three most common cloud types (congestus, deep, and stratiform) in tropical convective systems. In this present study, a new cloud type, namely shallow cloud, is included along with the existing three cloud types to make the model more realistic. Further, the cloud population statistics of four cloud types (shallow, congestus, deep, and stratiform) are taken from Indian (Mandhardev) radar observations. A Bayesian inference technique is used here to generate key time scale parameters required for the SMCM as SMCM is most sensitive to these time scale parameters as reported in many earlier studies. An attempt has been made here for better representing organized convection in GCMs, the SMCM parameterization is adopted in one of the state-of-art GCMs namely the Climate Forecast System version 2 (CFSv2) in lieu of the pre-existing simplified Arakawa–Schubert (default) cumulus scheme and has shown important improvements in key large-scale features of tropical convection such as intraseasonal wave disturbances, cloud statistics, and rainfall variability. This study also shows the need for further calibration the SMCM with rigorous observations for the betterment of the model’s performance in short term weather and climate scale predictions.

Kumar Roy is now working as a PIMS Postdoctoral Fellow with Prof. Boualem Khouider at Department of Mathematics and Statistics, University of Victoria. His current research topic is in the area of climate change modelling focusing on Stochastic models for clouds and tropical convection parameterization. He completed his PhD degree in Meteorology and Oceanography from Andhra University, India in March 2022 and his research has been carried out at Indian Institute of Tropical Meteorology (IITM), Pune, India. His research focuses on the development and application of sub-grid scale cloud models in numerical weather prediction (NWP) models, as well as how these models affect the forecasting abilities of NWP models.

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.**