Given integers $k,l$ and a graph $G$, how large can be the fraction of $k$-vertex subsets of $G$ which span exactly $l$ edges? The systematic study of this very natural question was recently initiated by Alon, Hefetz, Krivelevich and Tyomkyn who also proposed several interesting conjectures on this topic. In this talk we discuss a theorem […]
Understanding how fluid flows through heterogeneous materials, and how it can make these materials fail, are among the hardest challenges in materials science. Experiments and simulations show that flow through […]
Candidate for Assistant Professor in Mathematics, Scripps College A surprising application of mathematics: How to name a color Your brain likes patterns and categories; by grouping related ideas together, it can store and recall information quickly. Real-life continuous domains (like time and taste) are inherently composed of infinitely many points of information, which your brain […]
An agent comes to a fork in a road. There is a sign that says that one of the two roads leads to prosperity and another to death. The agent must take the fork, but she does not know which road leads where. Does the agent have a strategy to get to prosperity? On one […]
Abstract: A great deal of my research journey has involved the study of m-ary partitions. These are integer partitions wherein each part must be a power of a fixed integer m > […]
In 1968, Milnor famously conjectured that the smooth 4-genus of the torus knot T(p,q) is given by (p-1)(q-1)/2. This conjecture was first verified by Kronheimer and Mrowka in 1993 and has received several other proofs since then. In this talk, we discuss a nonorientable analogue of this conjecture, first formulated by Josh Batson. We prove […]
Uniform Convergence is a one-woman play, written and performed by mathematics graduate student Corrine Yap. It juxtaposes the stories of two women trying to find their place in a white male-dominated academic world. The first is of historical Russian mathematician Sofia Kovalevskaya, who was lauded as a pioneer for women in science but only after […]
Measurement error, formally defined as the difference between the measured value and the true value of a quantity of interest, is ubiquitous. When a doctor takes your blood pressure, the instrumentation may not be properly calibrated and the reading is subject to error. When completing an online Harry Potter Sorting Hat quiz, you may accidentally […]
Job Talk: Christina Edholm, University of Tennessee "Epidemiological models examining two susceptible classes" Monday, February 25 4:00-4:50pm Balch 218, Scripps College
Modular forms are ubiquitous in modern number theory. For instance, showing that elliptic curves are secretly modular forms was the key to the proof of Fermat's Last Theorem. In addition […]
Abstract: Whether enjoying the lucid prose of a favorite author or slogging through some other writer's cumbersome, heavy-set prattle (full of parentheses, em-dashes, compound adjectives, and Oxford commas), readers will […]
One foundational pillar of low dimensional topology is the connection between link invariants and 3-manifold invariants. One generalization of this has been given by Reshetikhin and Turaev to a surgery theory for colored ribbon graphs. Then to complete the analogy rather than 3-manifold invariants we now have a 2+1 dimensional topology quantum field theory (TQFT). […]
