Noah Cryns
Adolescence is a time of increased risk taking, novelty seeking, and exploration. These behaviors may have an adaptive function to facilitate dispersal from the natal nest but may also have relevance to addiction and morbidity in adolescence. Dopamine(DA) in the striatum is a likely candidate mediating such behavioral changes. However, studies investigating dopamine systems have often focused on adult mice and consummatory behavior. My goal is to design a study to better isolate the role of dopamine in adolescent dispersal behavior. To do this I will study exploratory locomotion in […]
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 […]
Joshua Lin
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 […]
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 […]
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 […]
Rahul Jain
Numerical linear algebra underlies much of the modern world. It is essential to a wide variety 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 been […]
Hunter Martin
One of the principal probes of cosmology is weak gravitational lensing whereby gravitational effects of mass bend the path of light. This causes small but correlated distortions in the images of distant galaxies which we can measure and then use to study the distribution of matter over cosmological distances and time scales. However, one of the fundamental assumptions of this method is that galaxy shapes (which we can model as ellipses) are randomly oriented in the universe, and that these distortions serve to align them. But what happens when the […]
Michelle Lee
If a nuclear weapon exploded in an urban environment, the effects would be catastrophic. Governments would want to quickly know what type of weapon it was, where it came from and who made it. One effect of the explosion is that it would expose many materials to large numbers of neutrons producing a variety of radioactive isotopes. When these isotopes decay, they produce characteristic gamma rays that allow them to be uniquely identified. My project will identify the radioactive species produced by neutron interactions with a wide variety of materials […]
Shea Khyeam
Although animals such as zebrafish and newborn mice retain the ability to regenerate the heart post-injury, adult mammalians have largely lost this cardiac regenerative capacity. Consequently, a patient will irreversibly lose as many as a billion cardiomyocytes following a heart attack and suffer from permanently reduced cardiac function. Today, nearly five million Americans live with heart failurethis underscores the significance of our inability to regenerate myocardial tissue. Most mammalian cardiomyocytes lose their proliferative and regenerative abilities because they undergo binucleation, terminal differentiation, and permanent withdrawal from the cell cycle postnatally. […]
Amy Zhang
The precise regulation of gene expression programs is fundamental for all cellular processes. The control of gene expression involving transcriptional activation and/or transcriptional repression is achieved by highly specific protein complexes. The aim of my work is to understand the mechanistic details of the yeast transcription repressor, the SIR complex, which is made up of three proteins: Sir2, Sir3, and Sir4. The SIR complex is critical for the epigenetic regulation of gene expression and the maintenance of chromosome stability. The comparative analysis of the different mechanisms of transcription repression processes […]