Peter Connick
Over the summer, we propose to investigate the root multiplicities of (generalized) Kac-Moody Algebras. Our plan is to create an open-source computer package that allows for the computation of root multiplicities of Kac-Moody algebras, building upon the existing tools available to computational mathematicians, for instance, the popular library sage-math. Once we have developed and verified this package against known tables of root multiplicities, we aim to start investigating the root multiplicities of simple graphs, and attempt to address some outstanding conjectures on the distributions of root multiplicities. A greater understanding […]
James Pierce
The geological core of North America, known as Laurentia, is a product of a collision that occurred some 1.85 billion years ago. The Superior Craton of eastern Canada collided with the Hearne and Wyoming Cratons to the west, creating the Trans-Hudson Orogenic Belt and the foundation for Earths putative first supercontinent, Nuna. As igneous rocks form, they record the direction and magnitude of Earths magnetic field as remanent magnetism. Ferromagnetic minerals, such as magnetite, align their magnetization in the direction of the prevailing magnetic field. After collecting samples that date […]
Jaime Zendejas
My research will focus on the development of a digital acoustic noise cancellation system. The system will be capable of taking recorded data, that has some amount of noise due to acoustic interference on it, and removing said noise from the data without affecting the data in any other way. This type of system is widely applicable to work done in many different STEM fields, but has particular importance in the field of physics. Many research projects in the field use some form of measurement of energy deposited into a […]
Jinen (Timothy) Guo
Quantum algorithms that take advantage of principles of quantum mechanics are able to solve certain problems (e.g. factorization of a large integer) much more efficiently than classical algorithms. One of the most promising candidates for qubit (the equivalent of a classical bit in quantum computing) implementation is the trapped ion. Although there have been promising results in trapped ion quantum information processing (QIP), it involves extensive use of lasers in cooling, readout, and qubit operations, which makes it challenging to scale up the system to many qubits. My research will […]
Hongli (Bob) Zhao
From modeling cardiovascular circulation, to designing power grids or complex financial derivative products, the study of how noise influences a probabilistic system’s state is vital for successful financial, biological and physical models. Uncertainty quantification aims to explore how uncertainty is propagated throughout computational models via constitutive laws of dynamics. Building upon previous literature, I start by focusing on coupled stochastic balance laws on each edge of a network, whose numerical characterizations of the solution can be achieved with the PDF method. On the other hand, the derivations are problem dependent […]
Mason Haberle
Numerical linear algebra underlies much of the modern world. It is essential to a wide variety of situations, and, as such, it is of great interest to analyze and optimize the underlying algorithms. In recent years, there has been an increased interest in optimizing algorithms to reduce communication, which is frequently many orders of magnitude slower than performing calculations. The Hlder-Brascamp-Lieb inequality and the Red-Blue Pebbling Game are two powerful approaches to theoretical analysis of communication, and both are used to derive communication optimal lower bounds. Once these bounds have […]
Andy Zhang
In our research, we will use toric geometry to study the cohomological structure of complex Grassmannians. The cohomology ring of a Grassmannian varieties is described by the Littlewood-Richardson rule. One of the main open questions in Schubert calculus concerns the generalization of the Littlewood-Richardson rule to flag varieties. Such a generalization is highly desirable, because it is a manifestly positive formula that can be applied to other areas: in algebraic geometry, it helps describe complicated intersections; in representation theory, it helps to find irreducible, direct-sum decompositions of tensor products; in […]
Siddharth Chittaranjan
Microbes pose a wide spectrum of nonpathogenic and pathogenic challenges for the immune system. The encounters are governed by the interactions between the bacteriums adaptations and the hosts ability to mount a protective immune response. Chlamydia trachomatis (Ct) is an especially unique pathogen as the infections it causes in the genital tract are typically asymptomatic. While this suggests that Ct possesses an effective set of tools to cloak itself as a lesser threat to the immune system, these tools still vary in success, as Ct strains elicit different immune responses […]
Yonna Kim
Solid-state defect centers such as the nitrogen-vacancy (NV) center in diamond are promising nanoscale quantum sensors capable of operating at extreme pressures and temperatures. Their sensitivity to magnetic field noise allows for the characterization of a wide range of dynamical phenomena arising from charge, spin, and phonon fluctuations in correlated matter. The frequency dependence of these fluctuations encodes unique information about the underlying physics processes that cannot be gleaned from the static signatures that are typically used in standard magnetometry. With NV centers, one could measure the magnetic response of […]
Arya Haghighi
The inhibition of glutathione, a buffer which maintains redox balance in neural cells, has recently been implicated as part of the pathology of multiple sclerosis (MS), a chronic and debilitating neurological disease. Magnetic resonance spectroscopy is a non-invasive technique which can quantitatively measure glutathione, amongst other metabolites, in the brain using the semi-localized by adiabatic selective refocusing sequence (SLASER) and J-Difference Editing (JDE). This proposal aims to apply this technique to image the concentration of various metabolites implicated in the regulation of redox potentials in the central nervous system on […]