### Cancelled due to COVID-19: Mihai Ciucu

- Series
- Combinatorics Seminar
- Time
- Friday, March 13, 2020 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 005
- Speaker
- Mihai Ciucu – Indiana University Bloomington

Cancelled due to COVID-19

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- Series
- Combinatorics Seminar
- Time
- Friday, March 13, 2020 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 005
- Speaker
- Mihai Ciucu – Indiana University Bloomington

Cancelled due to COVID-19

- Series
- ACO Student Seminar
- Time
- Friday, March 13, 2020 - 13:05 for 1 hour (actually 50 minutes)
- Location
- Skiles 005
- Speaker
- Jad Salem – Math, Georgia Tech – jsalem7@gatech.edu

Optimization and machine learning algorithms often use real-world data that has been generated through complex socio-economic and behavioral processes. This data, however, is noisy, and naturally encodes difficult-to-quantify systemic biases. In this work, we model and address bias in the secretary problem, which has applications in hiring. We assume that utilities of candidates are scaled by unknown bias factors, perhaps depending on demographic information, and show that bias-agnostic algorithms are suboptimal in terms of utility and fairness. We propose bias-aware algorithms that achieve certain notions of fairness, while achieving order-optimal competitive ratios in several settings.

- Series
- Stochastics Seminar
- Time
- Thursday, March 12, 2020 - 15:05 for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker
- Julian Gold – Northwestern University – gold@math.northwestern.edu

The pure spherical p-spin model is a Gaussian random polynomial H of degree p on an N-dimensional sphere, with N large. The sphere is viewed as the state space of a physical system with many degrees of freedom, and the random function H is interpreted as a smooth assignment of energy to each state, i.e. as an energy landscape.

In 2012, Auffinger, Ben Arous and Cerny used the Kac-Rice formula to count the average number of critical points of H having a given index, and with energy below a given value. This number is exponentially large in N for p > 2, and the rate of growth itself is a function of the index chosen and of the energy cutoff. This function, called the complexity, reveals interesting topological information about the landscape H: it was shown that below an energy threshold marking the bottom of the landscape, all critical points are local minima or saddles with an index not diverging with N. It was shown that these finite-index saddles have an interesting nested structure, despite their number being exponentially dominated by minima up to the energy threshold. The total complexity (considering critical points of any index) was shown to be positive at energies close to the lowest. Thus, at least from the perspective of the average number of critical points, these random landscapes are very non-convex. The high-dimensional and rugged aspects of these landscapes make them relevant to the folding of large molecules and the performance of neural nets.

Subag made a remarkable contribution in 2017, when he used a second-moment approach to show that the total number of critical points concentrates around its mean. In light of the above, when considering critical points near the bottom of the landscape, we can view Subag's result as a statement about the concentration of the number of local minima. His result demonstrated that the typical behavior of the minima reflects their average behavior. We complete the picture for the bottom of the landscape by showing that the number of critical points of any finite index concentrates around its mean. This information is important to studying associated dynamics, for instance navigation between local minima. Joint work with Antonio Auffinger and Yi Gu at Northwestern.

- Series
- Math Physics Seminar
- Time
- Thursday, March 12, 2020 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 005
- Speaker
- Wei Li – Louisiana State University – liwei@lsu.edu

The Neumann-Poincaré (NP) operator arises in boundary value problems, and plays an important role in material design, signal amplification, particle detection, etc. The spectrum of the NP operator on domains with corners was studied by Carleman before tools for rigorous discussion were created, and received a lot of attention in the past ten years. In this talk, I will present our discovery and verification of eigenvalues embedded in the continuous spectrum of this operator. The main ideas are decoupling of spaces by symmetry and construction of approximate eigenvalues. This is based on two works with Stephen Shipman and Karl-Mikael Perfekt.

- Series
- School of Mathematics Colloquium
- Time
- Thursday, March 12, 2020 - 11:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker
- Oscar Bruno – Caltech, Computing and Mathematical Sciences

- Series
- High Dimensional Seminar
- Time
- Wednesday, March 11, 2020 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker
- Santosh Vempala – Georgia Tech

**Please Note:** We give an efficient algorithm for robustly clustering of a mixture of two arbitrary Gaussians,
a central open problem in the theory of computationally efficient robust estimation, assuming
only that the the means of the component Gaussians are well-separated or their covariances are
well-separated. Our algorithm and analysis extend naturally to robustly clustering mixtures of
well-separated logconcave distributions. The mean separation required is close to the smallest
possible to guarantee that most of the measure of the component Gaussians can be separated
by some hyperplane (for covariances, it is the same condition in the second degree polynomial
kernel). Our main tools are a new identifiability criterion based on isotropic position, and a
corresponding Sum-of-Squares convex programming relaxation. This is joint work with He Jia.

- Series
- Geometry Topology Student Seminar
- Time
- Wednesday, March 11, 2020 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker
- Xingyu Zhu – Georgia Tech

In this talk we will survey some of the developments of Cheeger and Colding’s conjecture on a sequence of n dimensional manifolds with uniform two sides Ricci Curvature bound, investigated by Anderson, Tian, Cheeger, Colding and Naber among others. The conjecture states that every Gromov-Hausdorff limit of the above-mentioned sequence, which is a metric space with singularities, has the singular set with Hausdorff codimension at least 4. This conjecture was proved by Colding-Naber in 2014, where the ideas and techniques like \epsilon-regularity theory, almost splitting and quantitative stratification were extensively used. I will give an introduction of the background of the conjecture and talk about the idea of the part of the proof that deals with codimension 2 singularities.

- Series
- Analysis Seminar
- Time
- Wednesday, March 11, 2020 - 13:55 for 1 hour (actually 50 minutes)
- Location
- Skiles 005
- Speaker
- Isabelle Chalendar – Université Paris-Est - Marne-la-Vallée

Form methods are most efficient to prove generation theorems for semigroups but also for proving selfadjointness. So far those theorems are based on a coercivity notion which allows the use of the Lax-Milgram Lemma. Here we consider weaker "essential" versions of coerciveness which already suffice to obtain the generator of a semigroup S or a selfadjoint operator. We also show that one of these properties, namely essentially positive coerciveness implies a very special asymptotic behaviour of S, namely asymptotic compactness; i.e. that $\dist(S(t),{\mathcal K}(H))\to 0$ as $t\to\infty$, where ${\mathcal K}(H)$ denotes the space of all compact operators on the underlying Hilbert space.

- Series
- Time
- Wednesday, March 11, 2020 - 13:55 for 1 hour (actually 50 minutes)
- Location
- Skiles 005
- Speaker
- Isabelle Chalendar – Université Paris-Est - Marne-la-Vallée

Abstract: Form methods are most efficient to prove generation theorems for semigroups but also for proving selfadjointness. So far those theorems are based on a coercivity notion which allows the use of the Lax-Milgram Lemma. Here we consider weaker "essential" versions of coerciveness which already suffice to obtain the generator of a semigroup S or a selfadjoint operator. We also show that one of these properties, namely essentially positive coerciveness implies a very special asymptotic behaviour of S, namely asymptotic compactness; i.e. that $\dist(S(t),{\mathcal K}(H))\to 0$ as $t\to\infty$, where ${\mathcal K}(H)$ denotes the space of all compact operators on the underlying Hilbert space.

- Series
- Mathematical Biology Seminar
- Time
- Wednesday, March 11, 2020 - 11:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker
- Ralf Bundschuh – The Ohio State University

The prediction of RNA secondary structures from sequence is a well developed task in computational RNA Biology. However, in a cellular environment RNA molecules are not isolated but rather interact with a multitude of proteins. RNA secondary structure affects those interactions with proteins and vice versa proteins binding the RNA affect its secondary structure. We have extended the dynamic programming approaches traditionally used to quantify the ensemble of RNA secondary structures in solution to incorporate protein-RNA interactions and thus quantify these effects of protein-RNA interactions and RNA secondary structure on each other. Using this approach we demonstrate that taking into account RNA secondary structure improves predictions of protein affinities from RNA sequence, that RNA secondary structures mediate cooperativity between different proteins binding the same RNA molecule, and that sequence variations (such as Single Nucleotide Polymorphisms) can affect protein affinity at a distance mediated by RNA secondary structures.

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