Mounika Gopi
Meiosis, the method by which diploid cells produce haploid gametes, is a dramatic cellular remodeling event. This process is regulated by many transcriptional and translational changes, including the expression of longer, meiosis-specific mRNA isoforms. Superoxide dismutase 1 is a highly conserved and vital enzyme that fights against oxidative stress. During meiosis, budding yeast cells (Saccharomyces cerevisiae) produce a non-canonical mRNA isoform of SOD1 that is four times as long as the canonical mitotic mRNA, one of the largest differences in isoforms observed. The expression of the longform mRNA also correlates […]
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 […]
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 […]
Zitong Yang
The explosively growing size of data in cyberspace with low-value density creates a pressing need for data processing, information extracting, and knowledge refinement. Many applications thus appear, such as personalized recommendation and pinpointing advertisement, by exploring hidden value behind massive amounts of data. More concretely, my project considers the problem of learning a complete (orthogonal) dictionary from sparsely generated sample signals. Unlike conventional methods that minimize one norm to exploit sparsity and learn the dictionary one column at a time, we propose an alternative sparse promoting operator to learn the […]
Namrata Ramesh
Superlattices of colloidal nanocrystals are a new class of materials that have been made to self-assemble from a liquid suspension. Their high compositional tunability results in a range of electronic, optical, and mechanical properties. Strong coupling of nanocrystals in the superlattice – a very recent advance – leads to dramatic changes in their energy levels and, consequently, their optical properties. Particularly in semiconductor nanocrystal superlattices, understanding how the coupling of nanocrystals affects the optical gap will fine-tune these already promising optoelectronic materials for many applications. This, along with the comparatively […]
Susana Torres-Londono
For my research, I will use a computer simulation to predict the macroscopic behaviour of a material, FeCoNbS2, by making assumptions about its microscopics. To do this, I will use the Monte Carlo method to simulate FeCoNbS2’s magnetism. The Monte Carlo method is a random sampling algorithm that has been applied to everything from investment banking to climate change models. Magnetism is a fundamental physical phenomena that has vast implications in computer and circuit technology. Thus, studying magnetism using the Monte Carlo method is a pretty interesting task which combines […]
Zihao Li
In the past few decades, due to the strict implementation of the one-child policy in China, it had been almost impossible to conduct any research related to having a second child. However, China has been gradually relaxing this policy. Since November 2011, parents who are both the only child in their families may have two children. Since December 2013, couples in which only one parent is the only child may have two children. Finally, since October 2015, all couples are allowed to have two children. This policy change provides a […]
Chris Randall
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 […]
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 […]