Date/Time : 24 Mar 2022 15:00
Venue : via Zoom
Speaker : Patrick Rebeschini, Oxford University

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Meeting ID: 977 560 6531
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The local Rademacher complexity framework is one of the most successful general-purpose toolboxes for establishing sharp excess risk bounds for statistical estimators based on the framework of empirical risk minimization. Applying this toolbox typically requires using the Bernstein condition, which often restricts applicability to convex and proper settings. Recent years have witnessed several examples of problems where optimal statistical performance is only achievable via non-convex and improper estimators originating from aggregation theory, including the fundamental problem of model selection. These examples are currently outside of the reach of the classical localization theory.

In this work, we build upon the recent approach to localization via offset Rademacher complexities, for which a general high-probability theory has yet to be established. Our main result is an exponential-tail excess risk bound expressed in terms of the offset Rademacher complexity that yields results at least as sharp as those obtainable via the classical theory. However, our bound applies under an estimator-dependent geometric condition (the “offset condition”) instead of the estimator-independent (but, in general, distribution-dependent) Bernstein condition on which the classical theory relies. Our results apply to improper prediction regimes not directly covered by the classical theory. (Based on joint work with V. Kanade and T. Vaškevičius)

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Date/Time : 23 Mar 2022 16:00
Venue : via Zoom
Speaker : Wu Guohua, Nanyang Technological University

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Meeting ID: 830 4925 8042
Passcode: 1729=x3+y3

Abstract:  In this talk, I will review some existing work on splittings of c.e. sets, and then present an ongoing paper on nonsplitting, a joint work with Downey. The main result is the following.

Theorem: There are c.e. sets A and B such that B is strictly Turing reducible to A and for any c.e. sets U, V, if U and V form a set-splitting of A, then one of them is Turing reducible to B.

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Date/Time : 22 Mar 2022 16:00
Venue : via Zoom
Speaker : Takahiro Shibata, National University of Singapore

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Meeting ID: 875 1147 6637
Passcode: 468399

Abstract: In this talk, we deal with finite quotients of abelian varieties (fqav for short), that is, the quotients of abelian varieties by finite group actions. We mainly focus on the positivity of the canonical divisor of such a variety. Those varieties with Q-linearly trivial (resp. anti-ample) canonical divisors are called Q-abelian varieties (resp. Q-Fano fqav). We gives characterizations of those varieties and see that they are building blocks of general fqav’s.

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Date/Time : 22 Mar 2022 14:00
Venue : S17 #06-11 (SR6)
Speaker : Jiajun Ma, Xiamen University

Abstract: The program of classification of primitive ideals in the universal enveloping algebra was completed by Barbasch-Vogan, Duflo, Lusztig, and Joseph in the 1980s. A representation of a real reductive group is called special unipotent if its annihilator idea is the maximal primitive ideal attached to a nilpotent orbit in its Langlands dual.

This talk will explain how to count the number of unipotent representations using coherent continuation representations. In the classical group case, we will relate the counting problem with painted partition and bipartition.

This is joint work with Dan Barbasch, Binyong Sun, and Chengbo Zhu.

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Date/Time : 21 Mar 2022 10:00
Venue : via Zoom
Speaker : Changhui Tan, University of South Carolina

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Meeting ID: 827 0370 0860
Passcode: 355647

Abstract: In this talk, I will discuss a family of traffic flow models. The classical Lighthill-Whitham-Richards model is known to have a finite time shock formation for all generic initial data, which represents the creation of traffic jams. I will introduce a family of nonlocal traffic flow models, with look-ahead interactions. These models can be derived from discrete cellular automata models.

We show an intriguing phenomenon that the nonlocal slowdown interactions prevent traffic jams, under suitable settings. This talk is based on joint works with Thomas Hamori, Yongki Lee and Yi Sun.

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Date/Time : 18 Mar 2022 10:00
Venue : via Zoom
Speaker : Yian Ma, University of California at San Diego

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Meeting ID: 977 560 6531
Passcode: 123321

Abstract:  I will introduce some recent progress towards understanding the scalability of Markov chain Monte Carlo (MCMC) methods and their comparative advantage with respect to variational inference. I will discuss an optimization perspective on the infinite dimensional probability space, where MCMC leverages stochastic sample paths while variational inference projects the probabilities onto a finite dimensional parameter space. Three ingredients will be the focus of this discussion: non-convexity, dimension dependence, and stochasticity. This line of work is motivated by epidemic prediction, where we need uncertainty quantification for credible predictions and informed decision making with complex models and evolving data.

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Date/Time : 16 Mar 2022 16:00
Venue : via Zoom
Speaker : Leszek Kolodziejczyk, University of Warsaw

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Meeting ID: 830 4925 8042
Passcode: 1729=x3+y3

Abstract:  The Chong-Slaman-Yang construction of a model of RT^2_2 not satisfying Sigma^0_2-induction makes crucial use of a principle known as BME_1. This principle was later shown by Kreuzer and Yokoyama to be equivalent to WO(omega^omega), the statement that omega^omega is well-ordered.

I will talk about the following result: if A is any set in a model of RCA_0 + Sigma^0_2-collection such that Sigma_2(A)-induction fails, then there + is a descending sequence in omega^omega that is low in A. As a consequence, the negation of WO(omega^omega) is Pi11-conservative over RCA_0 +BSigma^0_2 + not-ISigma^0_2.

This result has some potentially interesting corollaries:

– If RCA_0 + RT^2_2 is Pi^1_1-conservative over BSigma^0_2, then this can be proved by considering only models in which BME_1 fails.

– The formula “X is a well-order” is not provably equivalent to any Sigma^1_1 formula over COH + BSigma^0_2 + not-ISigma^0_2. (In contrast, by earlier work of Fiori Carones, Wong, Yokoyama, and myself, the theory
WKL*_0 + not-ISigma^0_1, which is to some extent analogous to COH + BSigma^0_2 + not-ISigma^0_2, proves a collapse of the analytic hierarchy to Delta^1_1.)

– There exist two models of RCA_0 + COH + BSigma^0_2 that share a first-order universe and a common counterexample to ISigma^0_2 but are not elementarily equivalent. (In contrast, by the work of Fiori Carones et al. mentioned above, the families of Delta^0_2-definable sets of any such two models have to be elementarily equivalent.)

The conservativity result is a side product of a larger project joint with Fiori Carones, Yokoyama, and others.

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Date/Time : 15 Mar 2022 16:00
Venue : via Zoom
Speaker : Hugo Parlier, University of Luxembourg

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Meeting ID: 875 1147 6637
Passcode: 468399

Abstract: On closed surfaces of positive genus, through classical work of Dehn, simple closed curves can be described using intersection numbers. Now what if you want to describe curves with self-intersections in a similar way? This talk will be on joint work with Binbin Xu about this question, and where we end up constructing and studying so-called k-equivalent curves. These are distinct curves that intersect all curves with k self-intersections the same number of times.

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Date/Time : 15 Mar 2022 14:00
Venue : S17 #06-11 (SR6)
Speaker : Jiajun Ma, Xiamen University

Abstract: Consider theta correspondence of type I dual pair over a finite field F_q (q odd). Aubert-Michel-Rouquier deduced the explicit theta correspondence between unipotent representations for unitary groups using character theory and proposed a conjecture for the symplectic group-even orthogonal group pair. Following AMR’s approach, Shu-Yen Pan recently proved the conjecture using the combinatorics of symbols.

This talk will give a conceptually simpler approach to the question: directly compute the natural Hecke algebra module structure arising in the theta correspondence. We will see that the normalization of Hecke algebra is related to the first occurrence index, which leads to yet another proof of the conservation relation.

This is joint work with Jialiang Zhou and Congling Qiu.

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