we will start by giving a brief introduction to representation stability
and combinatorial categories. then we will introduce fulton and
macpherson's ``wonderful compactifications'' of configuration spaces,
and describe how they may be studied through the lens of representation
stability. in particular, we show that under a mild hypothesis we can
approach the representation theory of these spaces using the
combinatorial category $fs^{op}$. we end by discussing an attempt at
showing that these spaces do exhibit representation stability, although
to date the results of this approach have been fairly underwhelming.
this talk can be accessed at https://ucsd.zoom.us/j/309940113 .

entanglement is an essential component of quantum
computation, information, and communication. its applications range
from quantum key distribution and secret sharing to quantum
sensing. these applications drive the increasing need for a quantum
switching network that can supply end-to-end entangled states to
groups of endpoints that request them. to this end, i study a quantum
switch that distributes entanglement to users in a star topology. i
will present models for variants of this system and derive expressions
for switch capacity and the expected number of qubits stored in memory
at the switch.

much of this work focuses on bipartite entanglement switching. for
this case, i will discuss how performance metrics are affected by
decoherence and link heterogeneity. in this talk, i will also discuss
a work wherein we explore a set of switching policies for a switch
that can serve both bipartite and tripartite entangled states. i will
conclude the talk with a discussion of future research directions and
a long-term vision of leveraging tools from performance evaluation to
analyze and help guide the design of future quantum networks.\\

bio: gayane vardoyan is a phd candidate in the college of
information & computer sciences, at the university of massachusetts,
amherst. she is advised by prof. don towsley. she holds a b.s. in
electrical engineering and computer sciences from the university of
california, berkeley. her research interests include the performance
evaluation of classical and quantum communication systems.

she interned at inria, sophia antipolis during the summer of
2017. previously, she worked at the argonne national lab and the
computation institute at the university of chicago. she was a
participant of the rising stars 2019 academic career workshop for
women in eecs.

we shall discuss a classification result of gradient shrinking solitons.

the first demonstration of quantum supremacy in october
2019 was a major achievement of experimental physics. at the same
time, it relied on important developments in theoretical computer
science. in this talk i will describe my recent work laying the
complexity-theoretic foundations for google/ucsb's quantum supremacy
experiment, providing evidence that their device is exponentially
difficult to simulate with a classical computer. this crossroad
between complexity theory and quantum physics also offers new insights
into both disciplines. for example, i will describe how techniques
from quantum complexity theory can be used to settle purely classical
problems.

specifically, i will give a quantum argument which nearly resolves the
approximate degree composition conjecture, generalizing nearly 20
years of prior work. in a different direction, i will show that the
notion of computational pseudorandomness from complexity-based
cryptography has fundamental implications for black hole physics and
the theory of quantum gravity.\\

bio: adam bouland is a postdoctoral researcher in computer science
at the university of california, berkeley. he completed his ph.d. in
computer science at mit in 2017, where he was advised by scott
aaronson. prior to that he completed master's degrees in computer
science and mathematics at the university of cambridge, as well as a
b.s. in computer science/mathematics and physics at yale. his research
focuses on the theory of quantum computation and its connections with
classical complexity theory and physics.

grothendieck's section conjecture predicts that over arithmetically interesting fields (e.g. number fields or p-adic fields), rational points on a smooth projective curve x of genus at least 2 can be detected via the arithmetic of the etale fundamental group of x. we construct infinitely many curves of each genus satisfying the section conjecture in interesting ways, building on work of stix, harari, and szamuely. the main input to our result is an analysis of the degeneration of certain torsion cohomology classes on the moduli space of curves at various boundary components. this is (preliminary) joint work with padmavathi srinivasan, wanlin li, and nick salter.