CMU Mathematics Department Colloquia

Spring 2018

Organizer

• Department of Mathematics Colloquium Speaker Committee

• Because there might be a time delay in updating the webpage, please always check with the committee for the available dates.

Meeting Times

Refreshments take place 30 minutes prior to the talk.
Typical Colloquium Talks are Thursday, 4:00–4:50pm, in Pearce 227. Refreshments are in Pearce 216.
There might be some talks scheduled on a different day and time. The following table gives the most accurate information for each event.

Schedule

Abstracts

Speaker: Jordan Watts (January 30)
Title: Lie Group Actions and Differentiability Beyond Manifolds
Abstract: Lie group actions give a geometric way of understanding symmetry in a system, and considering the orbit space of such an action often simplifies the system. However, sometimes singularities appear in the orbit space. In order to continue doing analysis on the orbit space, one must first extend their perspective beyond smooth manifolds.
We will compare a few extensions of the category of smooth manifolds, and then return to Lie group actions to apply what we have learned. In particular, we will discuss a classification result for Lie group actions that locally look like finite group actions (orbifolds). We will then move over to symplectic quotients, and apply this classification result in order to extend a theorem of Herbig-Schwarz-Seaton: conditions under which a symplectic quotient is an orbit space of a Lie group action.
This talk is designed for a general mathematical audience; no prior knowledge of symplectic or algebraic geometry, invariant theory, etc., is required.

Speaker: Linda Furuto (March 1)
Title: Wayfinding through Ethnomathematics and the Malama Honua Worldwide Voyage
Abstract: Ethnomathematics is a pathway to real-world problem-solving that empowers individuals to be locally-minded, global citizens through a sense of purpose and a sense of place. Now in its 10th year, the Ethnomathematics and STEM Institute has explored learning and teaching practices via the innovative design, implementation, and assessment of culturally-sustaining work aligned with state and federal standards. Research has led to policy and practice implications, including becoming institutionalized as a new academic graduate program at the University of Hawai'i at Manoa. The mission, vision, and values of the Ethnomathematics Graduate Certificate/M.Ed. Mathematics Education are inspired by its role in the Malama Honua Worldwide Voyage of the traditional canoe Hokule'a, bridging Indigenous wisdom and 21st century learning in a shared commitment to equity, empowerment, and dignity for all.
Speaker's Bio Dr. Linda H.L. Furuto was born and raised in Hau'ula, O'ahu. She is a Professor of Mathematics Education at the University of Hawai'i at Manoa. Prior to joining UHM, Dr. Furuto was an Associate Professor of Mathematics and Head of Mathematics and Science at UH West O'ahu. Dr. Furuto completed her Ph.D. at UCLA, master's degree at Harvard University, and bachelor's degree at BYU. Research interests include: quantitative methodology, mathematics achievement, ethnomathematics, and access and equity. Dr. Furuto has been a Visiting Scholar of Mathematics at the University of Tokyo, worked in the Boston Public Schools as a research-practitioner in Harvard University's Inventing the Future project, taught secondary mathematics at the Fiji Technical College, and conducted research at the U.S. Department of State. She received the 2010 Pacific Business News' Top Forty Under 40 Award, 2011 UH Board of Regents Frances Davis Award for Excellence in Teaching, 2012 UH Board of Regents Medal for Excellence in Teaching, University of Hawai'i President's Green Initiative Award in 2017, and engaged in Hokule'a's Malama Honua Worldwide Voyage from 2013-2017 as education specialist and apprentice navigator.

Speaker: Sagun Chanillo (March 15)
Title: The Fundamental Theorem of Calculus and its Generalizations to Higher Dimension
Abstract: A basic consequence of the 1-variable fundamental theorem of calculus is that for a continuously differentiable function with compact support, one can control the size of the function by the integral of its derivative. Unfortunately this ceases to be true in higher dimensions. One has alternatives like the Moser-Trudinger inequality that plays a fundamental role in Conformal Geometry to the problem of prescribing Gauss curvature. Another alternative to the fundamental theorem of calculus in higher dimensions is the Gagliardo-Nirenberg inequality, which is equivalent to the isoperimetric inequality. In the last decade another inequality has been discovered by Bourgain and Brezis that is a standby for the fundamental theorem of calculus in higher dimensions. We will introduce these inequalities,and then show how the inequality of Bourgain-Brezis extends to the geometric setting of symmetric spaces. Symmetric spaces are manifolds equipped with a Riemannian metric, where for each point one has global isometries that fix the point and reverse geodesics through that point. The Poincare upper half plane, spheres are all examples. Lastly we give applications of the Bourgain-Brezis inequality to the 2-dimensional incompressible Navier-Stokes equation of Fluid Mechanics and the Maxwell equations of Electromagnetism. This is joint work with Po-lam Yung and Jean van Schaftingen.

Speaker: Vladimir Vinogradov (March 20)
Title: On Applications of Discrete Stable and Sibuya Distributions in the Theory of Branching and Related Processes
Abstract: We prove that a continuous-time branching particle system which starts from a discrete stable number of particles and is characterized by scaled Sibuya branching must have evolved from a Poisson field. We provide a local version of this result and derive other local limit theorems. Log-Laplace transforms of the marginals of the "high-density" limit of this system satisfy the semigroup property suggesting that it constitutes a continuous-state branching process with time-dependent positive stable marginals. We consider the "dual" subcritical Galton-Watson process constructed starting from a Galton-Watson process with scaled Sibuya branching conditioned by extinction. For the "dual" process, we derive pgf of the law of the total progeny. In a special case, we obtain its pmf and discover a relationship between this law and the distribution of a busy period of the server in the M/M/1 queue. We establish local approximation for the long-time evolution of a Poisson field of "dual" subcritical Galton-Watson processes with exponentially tilted Sibuya branching, and relate it to the logarithmically distributed Yaglom limit. We relate the extinction probability for supercritical Galton-Watson processes with discrete stable branching to the Lambert W function and its generalizations.