in k-12 school contexts, responsive math pedagogy typically refers to instruction where the teacher continuously elicits information about what 2022年亚洲世界杯预选赛 currently know and understand and responds in ways that move them forward in relation to developmental and grade-level mathematical goals. it is claimed that recognizing what 2022年亚洲世界杯预选赛 know and are able to do and leveraging that to move towards higher level reasoning and problem solving ensures equity and access to mathematics for all 2022年亚洲世界杯预选赛 . inspired by this approach, i discuss my teaching, research, and leadership efforts aimed at fostering a form of responsive pedagogy in collegiate math contexts. i discuss how these efforts can be relevant to mathematics teaching and learning at ucsd, especially in relation to increasing the retention and persistence of 2022年亚洲世界杯预选赛 from historically underrepresented backgrounds. 

ricci flow deforms the riemannian structure of a manifold in the direction of its ricci curvature and tends to regularize the metric. this provides useful information about the underlying space. ricci solitons are special solutions to the ricci flow and arise naturally in the singularity analysis of the flow. we shall discuss some curvature and entropy gap theorems of gradient ricci solitons. this talk is based on joint works with yongjia zhang and zilu ma, eric chen and man-chun lee.

a fleming-viot process is a system of n particles driven by independent copies of a driving markov process. when one of the particles hits the boundary of the domain, it is killed, and some other particle branches. there is only one infinite path (spine) in the branching structure. under some assumptions, when n goes to infinity, the distribution of the spine converges to the distribution of the driving markov process conditioned to avoid the boundary of the domain forever. 

based on joint articles with m. bieniek, j. englander, and t. tadic.

gene expression is the fundamental biological process by which rna and protein molecules are produced in a cell based on the information encoded in the dna. the regulation of gene expression dictates which genes are expressed and when, which is crucial for cells to perform specific functions and adapt to changes in their environment. single-cell experiments reveal that rna production occurs in bursts whose size and timing is random.  over the last thirty years, a plethora of mathematical models of stochastic gene expression have been developed in order to understand the origin of this noise. however, solving these models analytically becomes progressively more difficult as their complexity is increased. in this talk, i will show how many of these models can be solved using the queueing theory, which in turn can help us to solve the inverse problem of inferring the kinetics of gene expression from single-cell measurements of rna numbers.

we introduce a new lattice basis reduction algorithm with approximation guarantees analogous to the lll algorithm and practical performance that far exceeds the current state of the art. we achieve these results by iteratively applying precision management techniques within a recursive algorithm structure and show the stability of this approach. we analyze the asymptotic behavior of our algorithm, and show that the heuristic running time is $o(n^{\omega}(c+n)^{1+\varepsilon})$ for lattices of dimension $n$, $\omega\in (2,3]$ bounding the cost of size reduction, matrix multiplication, and qr factorization, and $c$ bounding the log of the condition number of the input basis $b$. this yields a running time of $o\left(n^\omega (p + n)^{1 + \varepsilon}\right)$ for precision $p = o(\log \|b\|_{max})$ in common applications. our algorithm is fully practical, and we have published our implementation. we experimentally validate our heuristic, give extensive benchmarks against numerous classes of cryptographic lattices, and show that our algorithm significantly outperforms existing implementations.

[pre-talk at 1:20pm]

in this talk, i will give an overview of some tools used in probabilistic combinatorics, and illustrate their use in two different projects. first, in joint work with marcus michelen and will perkins, we establish an asymptotic formula for the number of integer partitions of a general type: namely, partitions of an integer n where the sums of the kth powers of the parts are also fixed, for some collection of values k. second, in joint work with lina li and jinyoung park, we give enumerative and structural results for colorings of the middle layers of the hamming cube. this talk does not assume a lot of background, and it’s definitely okay if you don’t know much probability or combinatorics!

let $f_1,\ldots, f_r \in k[x_1,\ldots, x_n]$ be homogeneous polynomial of degree $d$. ananyan and
hochster (2016) proved that there exists a bound $n = n(r, d)$ where if collective strength
of $f_1, \ldots, f_r \geq n$, then $f_1, \ldots, f_r$ are regular sequence. in this paper, we study the explicit
bound $n(r, d)$ when $r = 3$ and $d = 2, 3$ and show that $n(3, 2) = 2$ and $n(3; 3) > 2$.