Scientific

We discuss deformation theory of rational curves and Mori’s famous Bend and Break techniques as well as their applications to Geometric Manin’s Conjecture. The lecture series contain introductory components as well as problem sessions and they aim for graduate students and postdocs.

We discuss deformation theory of rational curves and Mori’s famous Bend and Break techniques as well as their applications to Geometric Manin’s Conjecture. The lecture series contain introductory components as well as problem sessions and they aim for graduate students and postdocs.

We discuss deformation theory of rational curves and Mori’s famous Bend and Break techniques as well as their applications to Geometric Manin’s Conjecture. The lecture series contain introductory components as well as problem sessions and they aim for graduate students and postdocs.

During reproduction, viruses manufacture products that diffuse within the host cell. Because a virus does not have exclusive access to its own gene products, coinfection of multiple viruses allows for strategies of cooperation and defection— cooperators produce large amounts of gene product while defectors produce less product but specialize in appropriating a larger share of the common pool. Experimental data shows that, under conditions where coinfection is common, bacteriophage $\Phi$6 becomes trapped in a Prisoner’s dilemma, with defectors spreading to fixation, causing lowered population fitness. However, these experiments did not allow for fluctuation in the density of the external viral population. Here, I’ll discuss a model formulated to see if environmental feedback can free $\Phi$6 from the Prisoner’s dilemma. I’ll also discuss the concept of the Effective Game, which incorporates the frequency and density of different viral types in the environment.

The principal function of the nucleus is to facilitate storage, retrieval, and maintenance of the genetic information encoded into DNA and RNA sequences. A unique feature of nucleoplasm—the fluid of the nucleus—is that it contains chromatin (DNA) and RNA.

In contrast to other important biological polymer hydrogels, such as mucus and extracellular matrix, the nucleic acid polymers have a sequence. Recent experiments have shown that during the growth phase of the cell cycle, chromatin condenses in a sequence specific manner into regions within the nucleoplasm, possibly so that functionally related genes are grouped together spatially even though they might be far apart in terms of sequence distance.

At the same time, we are becoming increasingly aware of the role of liquid-liquid phase separation (LLPS) in cellular processes in the nucleus and the cytoplasm. Complex molecular interactions over a wide range of timescales can cause large biopolymers (RNA, protein, etc) to phase separate from the surrounding nucleoplasm into distinct biocondensates (spherical droplets in the simplest cases).

I will discuss recent work modelling the role of nuclear biocondensates in neurodegenerative disease and several ongoing projects related to
modelling and microscopy image analysis.