Siyang Li

Fast Radio Bursts (FRB) are high-energy millisecond duration radio signals of unknown astrophysical origins whose localizations are limited by the inherently low resolutions of radio telescopes. Recent theories propose that the origins of FRB may also produce nanosecond duration optical counterparts which, if observed with higher resolution optical telescopes, would allow astronomers to localize and identify the origins of FRB. Due to their extragalactic distances, optical counterparts to FRB can also be used to learn more about the fundamental properties and evolution of the Universe through probing the missing Baryonic matter in the Universe and the Epoch of Reionization. I will construct a telescope camera to search for these optical counterparts to FRB using state-of-the-art Silicon Photomultipliers (SiPM), which are p-n junction semiconductor photodetectors with nanosecond and single photon resolutions having significantly higher efficiencies, lower costs, and lower operating biases than traditional Photomultiplier Tubes. Upon completion, the SiPM camera will […]

Davy Deng

Listeria monocytogenes is a pathogen often found in poorly preserved food , especially dairy products. L. monocytogenes can survive with or without oxygen as well as inside or outside of host cells. During infection, L. monocytogenes must pass through the low-oxygen environment in the intestines before entering the high-oxygen target tissue. It thus stands to reason that both aerobic and anaerobic growth processes might be important for L. monocytogenes pathogenesis. Recently, it has been shown that essential components of aerobic respiration are critical for intracellular replication in vivo. However, the specific role of aerobic respiration within host cells remains unclear. Here, I propose conducting three experiments about the role of aerobic respiration in L. monocytogenes pathogenesis. I will use both forward and reverse genetic approaches, for which I will both analyze pathogenic phenotypes from gene functions and vice versa. Such bidirectional approaches allow me to probe for possible roles of […]

Maryn Sanders

The unique site of Antelope Valley River near Williams, California has for a few years been a place of interest and research because of the distinct sedimentary layering and the very regular pattern of hills and hollows. In the winter of 2017, a huge storm came through the site and induced four hundred landslides. Another storm then followed in the winter of 2019 at a much lesser degree of strength compared to the 2017 storm; however, it caused only about a hundred landslides, but all in new regions. The seemingly random nature of these slides has spiked my interests and pushed me to try to understand and to answer why some parts of the hills are failing, while others are not. I will be focusing on one hill in particular – Rhondas Hill – where a 2017 failure and a 2019 failure site lay side-by-side. To characterize and differentiate the […]

Junhao Fan

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 physics, it can be applied to calculate certain physical quantities. Our research aims to give a new, geometric proof of the Littlewood-Richardson rule,by applying toric degeneration to Weyl-group-translated Schubert varieties. More specifically, we will study the intersection behavior of Schubert varieties, in terms of face-intersections of Gelfand-Cetlin polytopes. A new geometric perspective would help give a deeper understanding of the […]

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 physics, it can be applied to calculate certain physical quantities. Our research aims to give a new, geometric proof of the Littlewood-Richardson rule,by applying toric degeneration to Weyl-group-translated Schubert varieties. More specifically, we will study the intersection behavior of Schubert varieties, in terms of face-intersections of Gelfand-Cetlin polytopes. A new geometric perspective would help give a deeper understanding of the […]

Noah Stevenson

Theoretical and experimental evidence suggests harnessing quantum mechanics to execute algorithms on qubit-based quantum hardware may allow for computation exponentially more powerful than is possible with classical computers. Characterizing how qubit states evolve in time is imperative for benchmarking quantum hardware; however, this has been difficult due to the inability to fully measure a quantum state without disrupting it. A solution is weak measurement, which recent work has improved for a single qubit by leveraging the data-processing power of a recurrent neural network (RNN). The time-evolution of qubits exchanging information with their environment over long time scales is not well understood, but must be characterized to implement efficient algorithms on a quantum processor. I propose to use weak measurement and deep learning models as filters to characterize the time-evolution of a superconducting qubit exchanging information with a simplified environment. My project will contribute to the fields ongoing research in determining […]

Aidan Backus

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 of the root multiplicities of Kac-Moody algebras would help with questions such as finding natural geometrical realizations of the algebras, and shed light on the connections that have already been found with mathematical physics. Some of these applications may include generalised knot invariants defined over Kac-Moody algebras rather than Lie Algebras, or the study of symmetries of systems and spaces […]

Diego A Pea

Laser cooling and trapping consists of using lights momentum to slow down and eventually confine atoms to small regions of space using light and magnetic fields. These techniques have been demonstrated with many elements in the periodic table, yet most transition metals are still to be addressed. A current effort in the Stamper-Kurn group seeks to implement laser cooling on titanium, eventually trapping and cooling it to quantum degeneracy. Cooling titanium requires that atoms exist in the a5F5 metastable state, an atomic internal state with energy higher than the ground state but with a relatively long lifetime compared to an excited state. One method of creating metastable titanium atoms is by optically pumping titanium from the ground state a3F4 to the y5G5 excited states where atoms can decay to the metastable state. My project focuses on characterizing the efficiency of such method of optical pumping using 379 nm and 844 […]

Yining Liu

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 physics, it can be applied to calculate certain physical quantities. Our research aims to give a new, geometric proof of the Littlewood-Richardson rule,by applying toric degeneration to Weyl-group-translated Schubert varieties. More specifically, we will study the intersection behavior of Schubert varieties, in terms of face-intersections of Gelfand-Cetlin polytopes. A new geometric perspective would help give a deeper understanding of the […]

Nikhil Sahoo

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 physics, it can be applied to calculate certain physical quantities. Our research aims to give a new, geometric proof of the Littlewood-Richardson rule,by applying toric degeneration to Weyl-group-translated Schubert varieties. More specifically, we will study the intersection behavior of Schubert varieties, in terms of face-intersections of Gelfand-Cetlin polytopes. A new geometric perspective would help give a deeper understanding of the […]