# Colloquium Series

## Flag varieties and variations on the Robinson-Schensted-Knuth correspondence

### Thursday, Nov 7, 2024 from 3:00-3:50 pm in UPH 275

#### Daniele Rosso, Indiana University Northwest

* Abstract: *The Robinson-Schensted correspondence (which was generalized by Knuth) is a combinatorial algorithm that gives a bijection between permutations and pairs of standard Young tableaux of the same shape. Steinberg and Spaltenstein observed that it can be interpreted in terms of the geometry of flags (increasing sequences of subspaces in a vector space). I will discuss some variations on this construction, some of them from joint work with V. Nandkumar and N. Saunders.

## 2024-2025 Colloquium Series

* Speaker/Affiliation: *Michel Gaspar, University of São Paulo

* Title: *How many colors does Borel need?

* Abstract:* The chromatic number of a graph is the minimum number of colors necessary to color

each vertex so that no two vertices forming an edge have the same color. By restricting

to colorings with definable properties, we obtain variants of the chromatic number. In

this talk, we will explore the "Borel chromatic number" of a graph, which can always be

defined for graphs whose set of vertices has a natural topology. We will see that, for

various natural mathematical structures, the independence phenomenon cannot be

avoided: for some graphs, one cannot always uniquely determine the values of their

Borel chromatic numbers.

Date/Time/Location:** Thursday, September 12, 2024** from

**3:00-3:50 pm**in

**UPH 275**

* Speaker/Affiliation: *Michał Wojciechowski, Institute of Mathematics Polish Academy of Sciences

* Title: *Unexpected approximation of Gaussian density and Hermite functions by B-splines

* Abstract:* We prove, and provide a quantitative error estimate, that a B-spline based on

essentially arbitrarily distributed knots approximates the Gaussian density. This

construction provides an unexpected inequality for any polynomial with distinct real

roots. On the other hand, one can see this as a kind of generalization of CLT for the

uniform distribution, which is exactly what arises for equally spaced knots. Moreover,

we prove that the approximation could be made in the Sobolev norms which leads

to analogous approximations of Hermite functions

The talk is based on a joint work with M. Rzeszut.

Date/Time/Location:** ***(Note the unusual day, time, and place)***Wednesday, September 18, 2024** from

**1:20-2:10 pm**in

**UPH 131**

* Speaker/Affiliation: *Martin J. Mohlenkamp, Ohio University

* Title: *The Hunt for the Swamp Monster

* Abstract:* There is a criminal on the loose in Tensorland. As innocent tensor approximation programs go about their work, sometimes they get ``swamped''. A swamped program has to work for many iterations without making appreciable progress before finally breaking free; sometimes they expire while trying. The criminal has been active since programs moved into Tensorland some 50 years ago, but has never been identified. Blurry images and indistinct tracks abound, leading to rumors and superstitions about the Swamp Monster. Join us as we construct and set a trap for the Swamp Monster. What will we find when the trap springs?

Date/Time/Location:** Thursday, October 3, 2024** from

**3:00-3:50 pm**in

**UPH 275**

* Speaker/Affiliation: *Borys Prydalnyi, Lutsk National Technical University, Lutsk, Ukraine

* Title: *Algorithms for the synthesis of complex technical systems with ill-defined parameters

* Abstract:* The work aims to improve the conditions for solving the problem of increasing the productivity and quality of the development of new technical systems in the context of the technological paradigm challenges of Industry 4.0 (and partly the prerequisites of the 5.0 paradigm). The research is focused on enhancing the conditions for automating the initial stages of technical systems creation, which encompass the formulation of its operational principles, structure, scheme, and design configuration. At present, these functions are carried out by a development engineer. In the studies, technical systems were conceptualized as an ordered set of structural elements and sustainable connections between them, which ensures the possibility of realizing their target functions. The main result of this research is the development of the preconditions of the theory for automated algorithmic structural-schematic synthesis of technical systems using a digital representation of their structural elements. To achieve this goal, the research project has established a set of principles for the digital representation of technical systems, a vector description of their structural elements, and the creation of databases of these elements. The use of vector representations of structural elements

allows the combination of structural elements and the generation of targeted structural schemes,

thereby enabling the achievement of the desired characteristics for the functioning of a given technical

system.

Date/Time/Location:** Wednesday, October 9, 2024** from

**1:25-2:15 pm**in

**UPH 235**

* Speaker/Affiliation: *Daniele Rosso, Indiana University Northwest

* Title:* Flag varieties and variations on the Robinson-Schensted-Knuth correspondence

* Abstract:* The Robinson-Schensted correspondence (which was generalized by Knuth) is a combinatorial algorithm that gives a bijection between permutations and pairs of standard Young tableaux of the same shape. Steinberg and Spaltenstein observed that it can be interpreted in terms of the geometry of flags (increasing sequences of subspaces in a vector space). I will discuss some variations on this construction, some of them from joint work with V. Nandkumar and N. Saunders.

Date/Time/Location:** Thursday, November 7, 2024** from

**3:00-3:50 pm**in

**UPH 275**

* Speaker/Affiliation: *Brett Mullins, UMass Amherst

* Title:* Efficient Marginal Reconstruction under Differential Privacy

* Abstract:* Differential privacy is the dominant standard for formal and quantifiable data privacy and has been used in major deployments that impact millions of people. Many differentially private mechanisms for query release and synthetic data contain steps that reconstruct answers to queries from answers to other queries privately measured. Reconstruction is an important subproblem for such mechanisms to economize the privacy budget, minimize error on reconstructed answers, and allow for scalability to high-dimensional datasets. In this talk, we introduce a principled and efficient postprocessing method ReM (Residuals-to-Marginals) for reconstructing answers to marginal queries under Gaussian noise. Our method builds on recent work on efficient mechanisms for marginal query release, based on making measurements using a residual query basis that admits efficient pseudoinversion, which is an important primitive used in reconstruction.

Date/Time/Location:** Thursday, November 14, 2024** from

**3:00-3:50 pm**in

**UPH 275**