Fall 2026

Spring 2026

Fall 2026

9/22/2026, Mon. 2:30-3:30 pm in White 324
Speaker: Jacob Hinds (CWRU)
Title: Quillen’s Q-construction
Abstract: In Quillen’s paper Higher Algebraic K-Theory, Quillen defines the K-theory of an Exact Category and proves that this definition coincides with the K-theory of Rings. In this talk we will discuss some of the main results of this paper. We will introduce the classifying space of a category and some of its fundamental properties, and then use this along with Quillen’s Q construction to define the K-theory of an Exact Category and prove some of its basic properties. If time permits, I will discuss Devissage and Localization theorems in Abelian Categories which will together produce a long exact sequence useful to computing the K-theory of the integers.

9/8/2026, Mon. 2:30-3:30 pm in White 324
Speaker: Runhan Wang (CWRU)
Title: Introduction to group cohomology
Abstract: Group cohomology provides a natural way to study group actions through homological algebra, and it appears throughout algebra and homotopy theory. In this talk, I will introduce group cohomology and its interpretation as an Ext group, with an emphasis on how these groups can be computed using projective resolutions and extensions. I will then explain how group cohomology arises naturally in the homotopy fixed point spectral sequence. As concrete examples, I will compute the mod-2 cohomology of C_2 and, more generally, of elementary abelian 2-groups (C_2)^n.

Fall 2026

10/2/2026, Fri. 3:30 pm in KHS 119
Speaker: Yiming Chen (CWRU)
Title: Gaussian-Process Emulators for Distribution-Valued Simulator Output
Abstract: An N-body planet-formation simulator returns, at each input θ, three observable distributions rather than a scalar. I emulate this map by transforming each distribution to its quantile function, compressing the three curves with joint MFPCA (six components, 92.3% of training variance), and modelling the scores with stationary and treed Gaussian processes. Across 124 design values, the treed GP on unsmoothed scores is the best tested candidate (balanced CRPS 0.2508 vs 0.2537 for a θ-free mean-density baseline). Score smoothing does not help, and the square-root vs quantile comparison depends on the metric. Reconstruction error is about one-twelfth of prediction error, so the bottleneck is predicting scores from θ under heavy realization noise. The outputs are non-Gaussian and clustered, the signal is weak, the score surfaces are locally non-stationary, and there are several related channels. These findings motivate my research direction: generalized, multi-output, non-stationary GPs for functional, replicated simulator output.

9/18/2026, Fri. 3:30 pm in KHS 119
Speaker: Angad Singh (CWRU)
Title: Modeling neurite mechanics in growth cones
Abstract: Directed neurite outgrowth depends on the balance between cytoskeletal forcing, bending resistance, and adhesion. The work models the neurite as an inextensible planar elastic rod with tip moment and follower-force loading. Mechanical equilibrium is solved using a damped Newton method, while growth and adhesion are modeled through a grow–bend–pin framework. Simulated curvature is compared with experimental results to investigate how growth-cone mechanics can produce persistent neurite turning and looping.

9/11/2026, Fri. 3:30 pm in KHS 119
Speaker: Quinnlan Aiken (CWRU)
Title: Immersed Boundary Simulation of Fast-Firing Extrusomes
Abstract: Fast-firing extrusomes are specialized organelles that rapidly discharge their contents upon receiving an appropriate stimulus. Among these, we consider the nematocyst, the stinging organelle of jellyfish. Nematocysts present a compelling subject for computational biofluid modeling due to the extreme discharge velocities occurring at micro-length scales. In this talk, we present a fluid-structure interaction model of nematocyst discharge using the Immersed Boundary Method, implemented via the open-source, HPC-optimized IBAMR software suite. We discuss the physical motivation for modeling these dynamics within a non-Newtonian fluid and outline ongoing and future research directions in high-speed extrusome simulation.

9/4/2026, Fri. 3:30 pm in KHS 119
Speaker: Brandon Oliva (CWRU)
Title: Illumination bodies for ball-convex bodies
Abstract: We introduce illumination bodies and weighted illumination bodies in the class of n-dimensional R-ball convex bodies. These bodies may be regarded as dual counterparts of the recently introduced R-ball floating bodies. We prove that the illumination bodies are convex. We also show that a left derivative of volume gives rise to a surface area measure for ball-convex bodies, the relative surface area measure. In dimension 2, we establish an isoperimetric inequality for this relative surface area.