Our events are free and open to the public unless otherwise noted. For additional information about events, seminars, lectures, colloquia, and related activities, call (716) 645-6284.

The Spring 2020 Event Listing is forthcoming.

**Faculty meeting**

4:00PM, Thu Jan 30 2020

**Faculty Meeting with Dean Schulze**

4:00PM, Tue Apr 7 2020, Room 250, Math Bldg

**General Faculty Meeting**

4:00PM, Thu Feb 7 2019, 250 Math

**Applied Math Happy Hour**

5:00PM, Fri Feb 8 2019, The Brick House Tavern and Tap -4120 Maple Rd, Amherst, NY 14226

**Graduate Mentoring Seminar- Dr. Dane Taylor**

Mathematics of Multilayer Networks for Data Science and Complex Systems

5:00PM, Tue Feb 19 2019, 250 Mathematics Building

**Algebra Seminar- Robert Kropholler, Tufts University**

An introduction to multiple context free groups.

4:00PM, Mon Mar 4 2019, 250 Mathematics Building

**Colloquium- Dr. Steven Mackey, Western Michigan University**

"Inverse Problems for Matrix Polynomials and Rational Matrices"

4:00PM, Thu Mar 7 2019, 250 Mathematics bldg.

**G&T Seminar**

Levi Sledd (Vanderbilt)

Asymptotic Dimension of Small Cancellation Groups

4:00PM, Fri Mar 8 2019, Math 122

**Applied Math Seminar- Alexandra Westley (UB)**

Solitary waves and collisions in the strongly nonlinear β-Fermi-Pasta-Ulam-Tsingou chain

3:50PM, Thu Mar 28 2019, 250 Mathematics Building

**Algebra Seminar- Ziqing Xiang, University of Georgia.**

On q-Schur algebras of classical type

4:00PM, Mon Apr 1 2019, 250 Mathematics Building

**Applied Math Seminar**

Cesar Aguilar, SUNY Geneseo

Anti-regular graphs as seen from within threshold graphs

3:50PM, Tue Apr 2 2019, 250 Mathematics Building

**Applied Math Seminar -**HAS BEEN RESCHEDULED TO 4/11/19** Cornelis van der Mee, University of Cagliari**

3:50PM, Tue Apr 9 2019, 250 Mathematics building

**Analysis Seminar-Xin Ma, Texas A&M University**

Paradoxical comparison and pure infiniteness of reduced crossed product C*-algebras.

4:00PM, Wed Apr 10 2019, 250 Mathematics Bldg.

**Applied Math Seminar**RESCHEDULED FROM 4/9/19** Cornelis van der Mee, University of Cagliari**

Cornelis van der Mee, University of Cagliari

3:50PM, Thu Apr 11 2019, 250 Mathematics Bldg.

**Algebra Seminar- Dr. Shilin Yu, Texas A&M University**

Deformation quantization of coadjoint orbits

4:00PM, Mon Apr 15 2019, 250 Mathematics Building

**Applied Math Seminar**

Nishant Malik, RIT

Triad Closure in Coevolving Network Systems

3:50PM, Tue Apr 16 2019, 250 Mathematics Building

**Analysis Seminar- Felipe García-Ramos, Universidad Autonoma de San Luis Potosi**

Topological hierarchy of dynamical systems with discrete spectrum

4:00PM, Wed Apr 17 2019, 250 Mathematics bldg.

**G&T Seminar**

Ruth Charney (Brandeis)

Outer Space for RAAGs

4:00PM, Fri Apr 19 2019, Math 122

**Analysis Seminar-Sebastián Barbieri, University of British Columbia**

How to find aperiodic subshifts on countable groups

4:00PM, Wed Apr 24 2019, 250 Math Bldg.

**Applied Math Seminar**

Richard Plotkin (UB Music)

Musical understanding with sets, groups, and distributions

3:50PM, Tue Apr 30 2019, 250 Mathematics Building

**Algebra Seminar- Piotr M. Hajac , IMPAN**

Pullbacks of graph C*-algebras from admissible intersections of graphs

4:00PM, Mon May 6 2019, 250 Mathematics Building

**Applied Math Seminar**

Stephen Lau, University of New Mexico

3:50PM, Tue May 7 2019, 250 Mathematics Building

**End of Semester Spring Faculty Meeting**

4:00PM, Thu May 9 2019, 250 Math Bldg.

**Cengage Webassign Presentation**

12:00PM, Fri May 10 2019, 250 Mathematics Bldg.

**G&T Seminar**

Hung Cong Tran (UGA)

On the relative hyperbolicity and manifold structure of certain right-angled Coxeter groups

4:00PM, Fri May 10 2019, Math 122

**New Graduate Student Orientation**

3:00PM, Thu Aug 22 2019, 250 Mathematics Building

**Test event in the past**

1:00PM, Sun Aug 25 2019, Math 150

**G&T Seminar**

Margaret Nichols (UB)

Taut sutured handlebodies as twisted homology products

4:00PM, Fri Sep 6 2019, 122 Mathematics Building

**Mariusz Tobolski, IMPAN (Alex Chirvasitu)**

4:00PM, Mon Sep 9 2019, math 250

**Naoki Masuda**

4:00PM, Tue Sep 10 2019

**Myhill lecture #1**

Laura DeMarco

4:00PM, Wed Sep 18 2019

**Myhill lecture #2**

Laura DeMarco

4:00PM, Thu Sep 19 2019

**Myhill Lecture #3**

Laura DeMarco

4:00PM, Fri Sep 20 2019

**Piotr Hajac, IMPAN; (Adam Sikora)**

4:00PM, Mon Sep 23 2019, Math 250

**Mariusz Tobolski (Hanfeng Li) Mathematics Polish Academy of Sciences**

Wednesday, September 25, 2019

**Colloquium: Piotr M. Hajac**

4:00PM, Thu Sep 26 2019

**Aparna Upadhyay, UB**

4:00PM, Mon Sep 30 2019, Math 250

**Kristofer Reyes (UB Department of Materials Design and Innovation)**

4:00PM, Tue Oct 1 2019, Math 250

**Yi Wang (Hanfeng Li)**

4:00PM, Wed Oct 2 2019, Math 250

**G&T Seminar**

Subhankar Dey (UB)

Cable knots are not thin

4:00PM, Fri Oct 4 2019, 122 Mathematics Building

**Applied math seminar: Erdem Sariyuce**

4:00PM, Tue Oct 8 2019

**Xiaocheng Li, University of Wisconsin**

An Estimate for Spherical Functions on SL(3, R)

4:00PM, Wed Oct 9 2019

**Quanlei Fang, CUNY BCC (Jingbo Xia)**

Revisiting Arveson’s Dirac operator of a commuting tuple

4:00PM, Wed Oct 16 2019, Room 250 Mathematics Bldg

**Colloquium: Barry Fox**

A Quant’s Journey Toward Diversification

4:00PM, Thu Oct 17 2019

**Applied math seminar: Mark Hoefer**

4:00PM, Tue Oct 22 2019

**Han Li, Wesleyan University ( Hanfeng Li)**

Masser’s conjecture on equivalence of integral quadratic forms

4:00PM, Wed Oct 23 2019

**G&T Seminar**

Thomas Ng (Temple)

Uniform exponential growth in nonpositive curvature

4:00PM, Fri Oct 25 2019, 122 Mathematics Building

**Chunlan Jiang, Hebei Normal University**

Similarity invariants of essentially normal Cowen-Douglas operators and Chern polynomials

4:00PM, Wed Oct 30 2019

**Alexandru Chirvasitu (UB)**

Loosely embeddable metric spaces

Wednesday, November 6, 2019, Room 250 Math Building; 4pm

**G&T Seminar**

Funda Gultepe (Toledo)

A Cannon-Thurston map for the surviving curve complex of a punctured surface.

4:00PM, Fri Nov 15 2019, 122 Mathematics Building

**Anita T. Layton (University of Waterloo)**

4:00PM, Tue Nov 19 2019

**Hui Dan (Fudan University)**

4:00PM, Wed Nov 20 2019, 250 Math Building; North campus

**Bernard Badzioch (UB)**

Teaching with Open edX

4:00PM, Fri Nov 22 2019, Room 250; Math Bldg

Note: Professor John Ringland was the faculty speaker at the College of Arts Commencement on Sunday, May 19, 2019. **See the video of Ringland's commencement address.**

**Winter Session Begins**

Thursday, January 4, 2018

**Martin Luther King, Jr.- Day Observed**

Monday, January 15, 2018

**Winter Session ends**

Wednesday, January 24, 2018

**Spring Classes Begin**

Monday, January 29, 2018

**Departmental Meeting- open forum with Chairman candidates**

4:00PM, Tue Jan 30 2018

**G&T Seminar**

Yulan Qing (University of Toronto)

4:00PM, Fri Feb 2 2018, Math 122

**Analysis Seminar- Jingbo Xia, UB**

A double commutant relation in the Calkin algebra on the Bergman space

4:00PM, Wed Feb 7 2018, 250 Mathematics

**Graduate Mentoring Seminar- Dr. Alexandru Chirvasitu**

5:00PM, Tue Feb 13 2018, Math 250

**Analysis Seminar- Weiran Sun, Simon Fraser University**

Global Well-Posedness of the Non-Cutoff Boltzmann Equation with Polynomial Decay Perturbations

4:00PM, Wed Feb 14 2018, 250 Math Bldg

**Algebra Seminar**

Jieru Zhu, University of Oklahoma

Two Boundary Centralizer Algebras for gl(m|n)

4:00PM, Mon Feb 19 2018, 250 Math Building

**Graduate Mentoring Seminar- Prof Dane Taylor, University at Buffalo**

** **Mathematics of multilayer networks for data science and complex systemsNetworks are a natural representation for datasets arising in biology (neuroscience, microbiomes and genetics), social systems (reality mining, politics and online social networks) and critical infrastructures (internet, power grid, and transportation system). Due in part to the diversity of applications, there remains a significant gap between the popular heuristics that are widely used for these systems and the development of rigorous techniques grounded on first principles in mathematics and statistics. I will describe my analyses of multilayer networks in which different layers encode different types of edges, such as complementary datatypes or a network at different instances in time. This research involves a variety of techniques (e.g., linear algebra, perturbation theory, random matrix theory, and computational topology/geometry) and is both applied and theoretical. For example, I will discuss the ranking of U.S. Mathematics Departments using data from the Mathematics Genealogy Project as well as describe the information-theoretic limitations on the detectability of communities in networks. I will focus on situations in which applied mathematics can have significant impact in network science as well as describe situations where the applications are demanding new mathematical methods.

5:00PM, Tue Feb 20 2018, 250 Math

**G&T seminar**

David Cohen (University of Chicago)

4:00PM, Fri Feb 23 2018

**Algebra Seminar- Xingting Wang, Temple University**

Noncommutative algebra from a geometric point of view

4:00PM, Mon Feb 26 2018, 250 Math Bldg.

**Algebra Seminar**

Liang Ze Wong, University of Washington

The Enriched Grothendieck Construction and Comodule Categories

4:00PM, Mon Mar 5 2018, 250 Math Building

**Applied Math Seminar- Guo Deng, UB**

3:45PM, Tue Mar 13 2018, Math 250

**Graduate Mentoring Seminar- Dr. Brian Hassard**

5:00PM, Tue Mar 13 2018, Math 250

WeBWork problems are authored in an interpreted language that combines elements of perl and of TeX, extended by libraries of perl code.

This talk will boot a WeBWork server from "live" USB stick and introduce WebWork programming by editing myTestCourse/Demo problem 3,

which asks students to differentiate a quadratic.

You will get the most out of the talk if you are able to work along on your own laptop with a "WeBWork live" USB stick.

If you give me a blank USB stick (4G or greater) in advance of the talk, I'll return it with a bootable image of

WW2.12_Ubuntu16.04_Vanilla_LiveDVD.iso ready to use during the talk.

**G&T Seminar**

Abdalrazzaq Zalloum (Buffalo)

Contracting geodesics in CAT(0) groups

Abstract: The geodesicity condition for Gromov delta hyperbolic groups is a coarse local condition, in other words, in order to check whether a given edge path is a geodesic you need only to check that subsegments of length m, where m depends on delta, are geodesics. The formal way of stating the above is to say that hyperbolic groups admit a regular language that reads all geodesics in the group. This seemingly simple observation has a lot of interesting consequences. For example, one can use it to show that hyperbolic groups have a rational growth function. Another consequence is the fact that the boundary of a hyperbolic group is a subshift of finite type (over Z). Charney and Sultan introduced the notion of contracting boundaries for CAT(0) spaces, in short, these are the collection of all "hyperbolic directions" in a CAT(0) space. This talk will be about our theorem with Josh Eike proving that contracting geodesics in CAT(0) groups are realized by a regular language.

4:00PM, Fri Mar 16 2018, Math 112

**Spring Recess**

Monday, March 19, 2018

**Classes Resume**

Monday, March 26, 2018

**Applied Math Seminar- Jiwei Zhao, SUNY Buffalo, Biostatistics**

3:45PM, Tue Mar 27 2018, Math 250

**Algebra Seminar- Ryo Kanda, Osaka University**

Normal extensions of Artin-Schelter regular algebras and flat families

4:00PM, Mon Apr 2 2018, 250 Math Building

**Colloquium- Barbara Prinari, University of Colorado, Colorado Springs**

4:00PM, Tue Apr 3 2018, 250 Mathematics Bldg.

**Analysis Seminar- Tsan Cheng Yu, SUNY at Buffalo**

4:00PM, Wed Apr 4 2018, 250 Mathematics Bldg.

**Faculty Meeting**

4:00PM, Thu Apr 5 2018, 250 Math Bldg.

**Algebra Seminar- Theo Johnson-Freyd, Perimeter Institute for Theoretical Physics**

Moonshine anomalies

4:00PM, Mon Apr 9 2018, 250 Math Building

**Analysis Seminar**

Nico Spronk, University of Waterloo

Idempotents, topologies and ideals

4:00PM, Wed Apr 11 2018, 250 Math Bldg.

**Algebra Seminar- Angelica Deibel, Brandeis university**

Random Coxeter Groups

4:00PM, Mon Apr 16 2018, 250 Math Bldg.

**Analysis Seminar**

Hanfeng Li, SUNY at Buffalo

Garden of Eden and specification

4:00PM, Wed Apr 18 2018, 250 Math Bldg.

**G&T Seminar**

Bill Menasco (Buffalo)

4:00PM, Fri Apr 20 2018, 122 Math

**Algebra Seminar- Joshua Eike from Brandeis University**

Regular Languages and Growth in Groups

4:00PM, Mon Apr 23 2018, 250 Math Building

**Applied Math/Complex Networks Seminar-Katharine (Kate) Anderson, Carnegie Mellon University**

Skill networks and measures of complex human capital

Abstract: We propose a novel, network-based method for measuring worker skills. We demonstrate the method using data from an online free- lance website. Using the tools of network analysis, we divide skills into endogenous categories based on their relationship with other skills in the market. Workers who specialize in these different areas earn dramatically different wages. We then show that in this mar- ket, network-based measures of human capital provide more insight into wages than traditional human capital measures. In particular, we show that workers with diverse skills earn higher wages than those with more specialized skills. Moreover, we can distinguish between two different types of workers benefiting from skill diversity: jacks- of-all-trades, whose skills can be applied independently on a wide range of jobs, and synergistic workers, whose skills are useful in combination and fill a hole in the labor market. On average, workers whose skills are synergistic earn more than jacks-of-all-trades. This framework has the potential to reduce friction in online job markets, improve employer-employee matches, and guide worker training and marketing decisions.

www.andrew.cmu.edu/~andersok

12:00PM, Wed Apr 25 2018, 108 Capen

**Tenured faculty meeting**

4:00PM, Thu Apr 26 2018, 250 Math Bldg.

**G&T Seminar**

Angelica Deibel (Brandeis)

Random Coxeter groups

4:00PM, Fri May 4 2018, 122 Math

**Algebra Seminar**

Shizhuo Zhang, Indiana University

Exceptional collections of line bundles and quiver moduli.

4:00PM, Mon May 7 2018, 250 Mathemtics Bldg.

**Analysis Seminar- Rostislav Grigorchuk, Texas A&M University**

Group of intermediate growth, aperiodic order, and Schroedinger operators.

4:00PM, Wed May 9 2018, 250 Math Bldg.

**Faculty Meeting**

4:00PM, Thu May 10 2018, Math 250

**Last Day of Classes**

Friday, May 11, 2018

**G&T Seminar**

Bill Menasco (Buffalo)

Distance and intersection number in the curve complex (Continued)

4:00PM, Fri May 11 2018, 122 Math

**Reading Days**

Saturday, May 12, 2018

**Reading Days**

Sunday, May 13, 2018

**Semester Finals Begin**

Monday, May 14, 2018

**Commencement Weekend**

Friday, May 18, 2018

**Algebra Seminar-Ben Webster, University of Waterloo**

Representation theory of symplectic singularities

4:00PM, Mon Aug 27 2018, 150 Mathematics Bldg.

**Faculty Meeting**

4:00PM, Thu Aug 30 2018, 250 Mathematics Bldg.

**Graduate Mentoring Seminar- Dr. William Menasco**

5:00PM, Tue Sep 4 2018, Math 250

**Analysis Seminar- Mariusz Tobolski, Institute of Mathematics Polish Academy of Sciences**

Local-triviality dimension of actions of compact quantum groups

Abstract: ** "Local-triviality dimension of actions of compact quantum groups" **

We introduce the local-triviality dimension of an action of a compact quantum group on a unital C*-algebra using completely positive contractive order zero maps of Winter and Zacharias. In the case of a compact Hausdorff group acting on a compact Hausdorff space our definition recovers the usual local triviality of a compact principal bundle.

Actions with finite local-triviality dimension are automatically free and there exists an analog of an n-universal bundle (in the sense of Steenrod) for any compact quantum group G. Our main motivating examples are the Matsumoto-Hopf fibration and the antipodal action on free orthogonal quantum sphere. As the main application, we prove a Borsuk-Ulam-type conjecture of Baum, Dąbrowski and Hajac in the case where the compact quantum group G admits a classical subgroup whose induced action has finite local-triviality dimension.

4:00PM, Wed Sep 5 2018, 150 Mathematics building

**G&T Seminar**

Ludwik Dąbrowski (SISSA)

The weak Hilbert-Smith conjecture from the Borsuk-Ulam type conjecture

4:00PM, Fri Sep 7 2018, 122 Math

**Applied Math Happy Hour**

5:00PM, Fri Sep 7 2018, Anchor Bar on corner of Maple and Sweethome Rd.

**Algebra Seminar-Piotr M. Hajac, IMPAN**

An equivariant pullback structure of trimmable graph c*-algebras

4:00PM, Mon Sep 10 2018, 150 Mathematics Bldg.

**Graduate Mentoring Seminar-Dr. Bernard Badzioch**

5:00PM, Tue Sep 11 2018, Math 250

**Analysis Seminar- Jianchao Wu, Penn State University**

Demystifying Rokhlin dimension and related notions

4:00PM, Wed Sep 12 2018, 150 Math Bldg

**Colloquium- Piotr M. Hajac (IMPAN) COLLOQUIUM HAS BEEN RESCHEDULED TO MONDAY 9/17/18, 4PM ROOM 150 MATH BLDG!!!**

Thursday, September 13, 2018,

**G&T Seminar**

Camille Horbez (CNRS/Fields Institute)

Growth under automorphisms of hyperbolic groups

4:00PM, Fri Sep 14 2018, 122 Math

**Colloquium- Piotr M. Hajac (IMPAN) PLEASE NOTE RESCHEDULED FROM 9/13**

OPERATOR ALGEBRAS THAT ONE CAN SEE

4:00PM, Mon Sep 17 2018, 150 Math Bldg.

**Applied Math Seminar**

Kenny Joseph (UB Computer Science) https://kennyjoseph.github.io/

Bayesian models of stereotyping and social categorization

3:50PM, Tue Sep 18 2018, 150 Math Bldg

**Graduate Mentoring Seminar- Dr. William Menasco**

5:00PM, Tue Sep 18 2018, Math 250

**Analysis Seminar**

Yi Wang, UB

Asymptotic stable division property and the Arveson-Douglas Conjecture.

4:00PM, Wed Sep 19 2018, 150 Math Bldg.

**Special Interdisciplinary Seminar- Ludwik Dabrowski (SISSA, Trieste)**

"Almost commutative geometry of the Standard Model"

3:00PM, Thu Sep 20 2018, 150 Math Bldg.

**Analysis Seminar- Benjamin Hayes, University of Virginia**

Local weak* convergence and the entropy of algebraic actions

4:00PM, Wed Sep 26 2018, 150 Math Bldg.

**Algebra Seminar- Changlong Zhong, University at Albany**

On the K-theoretic stable basis of Springer resolutions

4:00PM, Mon Oct 1 2018, 150 Mathematics Bldg.

**Applied Math Seminar- John Medaglia, Drexel University**

The Foundations and Frontiers of Cognitive Neuroengineering

3:50PM, Tue Oct 2 2018, 150 Math Bldg.

**G&T Seminar**

Kiyoshi Igusa (Brandeis)

Equivariant Hatcher construction

4:00PM, Fri Oct 5 2018, 122 Math

**Algebra Seminar**

Debashish Goswami Indian Statistical Institute

(No) quantum symmetry for compact connected smooth manifolds

4:00PM, Mon Oct 8 2018, 150 Mathematics Bldg.

**G&T Seminar**

Mahan Mj (Tata Institute/Fields Institute)

Bowen-Margulis measures and Extremal Cocycle Growth

4:00PM, Fri Oct 12 2018, Math 122

**Algebra Seminar- Gus Schrader, Columbia University**

Dehn twists and Whittaker functions

4:00PM, Mon Oct 15 2018, 150 Mathematics Bldg.

**Applied Math Seminar- James Chen, UB Mechanical and Aerospace Engineering)**

A Kinetic Description for Morphing Continuum

3:50PM, Tue Oct 16 2018, Math 150

**G&T Seminar**

Jing Tao (University of Oklahoma/Fields Institute)

Big Torelli groups

4:00PM, Fri Oct 19 2018, 122 Math

**Applied Math Seminar- Austin Benson, Cornell University**

Simplicial closure and simplicial diffusions

3:50PM, Tue Oct 30 2018, Math 150

**Graduate Mentoring Seminar- Dr. Adam Sikora**

5:00PM, Tue Oct 30 2018, Math 250

**Analysis Seminar- Alexandru Chirvasitu, SUNY at Buffalo**

Incompressibility of compact groups

4:00PM, Wed Oct 31 2018, 150 Math Bldg.

**Algebra Seminar-Vasu Tewari, University of Pennsylvania**

Divided symmetrization and generalized permutahedra

4:00PM, Mon Nov 5 2018, 150 Mathematics Bldg

**Applied Math Seminar- Francois Meyer, University of Colorado, Boulder**

Tracking the Evolution of Dynamic Networks

3:50PM, Tue Nov 6 2018, Math 150

**Graduate Mentoring Seminar- Mr. Fred Stoss, Librarian, Lockwood Library**

5:00PM, Tue Nov 6 2018, Math 250

**Algebra Seminar- Naihuan Jing, North Carolina State University**

Presentation of Yangian algebras in BCD types.

4:00PM, Mon Nov 12 2018, 150 Mathematics Bldg

**Applied Math Seminar- Hiroki Sayama, SUNY Binghamton**

Graph product multilayer networks: spectral properties and applications

3:50PM, Tue Nov 13 2018, Math 150

**Colloquium- Dr. Brian Hassard**

Grading from scanned exams with mark-recognition recorded scores:

4:00PM, Thu Nov 15 2018, Math 250

**G&T Seminar**

Bülent Tosun (Alabama)

Contact surgeries, symplectic fillings and Lagrangian discs

4:00PM, Fri Nov 16 2018, 122 Math

**G&T Seminar**

Jacob Russell (CUNY)

Convexity in Hierarchically Hyperbolic Spaces

4:00PM, Fri Nov 30 2018, 122 Math

**Dec 3 Algebra Seminar- S. Paul Smith, University of Washington**

Elliptic algebras

4:00PM, Mon Dec 3 2018, 150 Mathematics Bldg.

The algebras of the title form a flat family of (non-commutative!)

deformations of polynomial rings. They depend on a relatively prime

pair of integers n>k>0, an elliptic curve E, and a translation

automorphism of E. Quite a lot is known when n=3 and n=4 (and k=1),

in which case the algebras are deformations of the polynomial ring on

3 and 4 variables. These were discovered and have been closely studied

by Artin, Schelter, Tate, and Van den Bergh, and Sklyanin. They were

defined in full generality by Feigin and Odesskii around 1990 and

apart from their work at that time they have been little studied.

Their representation theory appears to be governed by, and best

understood in terms of, the geometry of embeddings of powers of E (and

related varieties like symmetric powers of E) in projective

spaces. Theta functions in several variables and mysterious identities

involving them provide a powerful technical tool.

This is a report on joint work with Alex Chirvasitu and Ryo Kanda.