[Professor Kachi's Graduate Student Advising]

I am currently an advisor of one graduate student, Mr. Chengzhen Fang .

Vita

[Professor Kachi's Recent talks]

[A] "In-house" talks

1. Colloquium (December 3, 2015),

• Title: Primes, zeta and asymptotic formulas

- Granville-Zagier's multi zeta values

Abstract

[B] By invitation

1. Colloquium at University of Missouri at Kansas City (November 13, 2015),

hosted by

• Professor Xianping Li (University of Missouri at Kansas City).

2. Zeta Institute Weekly Seminar at Tokyo Institute of Technology (May 26, 2014),

hosted by

• Professor Nobushige Kurokawa (Tokyo Institute of Technology).

[Preprint(s)]

• [1] Y. Kachi and P. Tzermias: "A formula for the Hurwitz zeta function, Riemann's functional equation and certain integral representations", preprint (2017), 21pp.

[Professor Kachi's List of Publications]

• [2] Y. Kachi and P. Tzermias: "On the m-ary partition numbers", Algebra and Discrete Mathematics, Vol. 19 (2015), No. 1, pp. 67-76.

• [3] Y. Kachi and P. Tzermias: "Infinite Products Involving zeta (3) and Catalan's Constant", Journal of Integer Sequences, Vol. 15 (2012), Article 12.9.4. (16pp.)

• [4] Y. Kachi: "Global smoothings of degenerate Del Pezzo surfaces with normal crossings", Journal of Algebra, Vol. 307 (2007), 249-253.

• [5] Y. Kachi and S.B. Mulay: "Local-to-Global Correspondence in Algebraic Geometry", Proceedings of Fano Conference (A. Conte, A. Collino, M. Marchisio, ed.) 2004, pp. 485-514.

• [6] Y. Kachi and E. Sato: "Segre's reflexivity and an inductive characterization of hyperquadrics", Memoirs of Amerian Mathematical Society, Number 763, 2002 (116pp.)

• [7] Y. Kachi and J. Kollar: "Characterization of P^n in arbitrary characteristic", Asian Journal of Mathematics, Vol. 4, No. 1, Special Volume in memory of K. Kodaira (2000), 115-122.

• [8] Y. Kachi and E. Sato: "Characterization of projective spaces and hyperquadrics", in Proceedings of Algebra Conference in memory of G. A. Kurosh, Moscow 1998 (Y. Bahturin, ed.), Walter de Gruyter, Berlin, 2000, pp. 155-165.

• [9] Y. Kachi and E. Sato: "Polarized varieties whose points are joined by rational curves of small degrees", Illinois Journal of Mathematics, 43, Vol. 2 (1999), 350-390.

• [10] Y. Kachi: "Flips from 4-folds with isolated complete intersection singularities", American Journal of Mathematics, 120 (1998), 43-102.

• [11] Y. Kachi: "Flips of semi-stable 4-folds whose degenerate fibers are union of Cartier divisors which are terminal factorial 3-folds", Mathematische Annalen, Vol. 307 (1997), 647-662.

• [12] Y. Kachi: "Extremal contractions from 4-dimensional manifolds to 3-folds", Annali della Scuola Normale Superiore di Pisa, Serie IV, XXIV, 1 (1997), 63-131.

[Professor Kachi's Editorial Experience]

• [13] "Recent Progress in Arithmetic and Algebraic Geometry", Contemporary Mathematics, Vol. 386 (Y. Kachi, S.B. Mulay and P. Tzermias, ed.) The American Mathematical Society, 2005 (172pp.)

• Contents:

• F. Campana and Q. Zhang, Compact Kaehler threefolds of (pi)_1-general type;

• S.D. Cutkosky and L. Ghezzi, Completions of valuation rings;

• A. Ebin, D. Hur, A. Katz and V. Shchogolev, A new construction of maximal curves;

• S.J. Kovacs, Strong non-isotriviality and rigidity;

• S.J. Kovacs, Spectral sequences associated to morphisms of locally free sheaves;

• T. Luo and Q. Zhang, Holomorphic forms on threefolds;

• K. Matsuki, A note on toroidarization: The problem of resolution of singluarities of morphisms in the logarithmic category;

• R.J. Pries, Jacobians of quotients of Artin-Schreier curves;

• K. Schwede, Gluing schemes and a scheme without closed points.

Ads: "New Publications Offered by the AMS", AMS Notices, November 2005.

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[Seminar organization]

I am the (sole) organizer of

• Algebraic Geometry/Analytic Number Theory Seminar.

[Professor Kachi's Brief profile]

I am a research mathematician (just like any other colleagues of mine in KU Mathematics Department).

• Algebraic Geometry (= Mathematics Subject Classification #14),

and

• Number Theory (= Mathematics Subject Classification #11).

My current research focuses on the interplay between these two subjects. Most

recently I have been working on the Riemann's zeta function, with my

(permanent) collaborator

• Professor Pavlos Tzermias at

Department of Mathematics, University of Patras, Greece .

infinite product formulas for some numbers involving two famous constants,

namely, the Catalan's constant and the Apery's constant (the latter is also

called zeta (3)).

(1/2) (pi) = ( (2*2)/(1*3) ) ( (4*4)/(3*5) ) ( (6*6)/(5*7) ) ( (8*8)/(7*9) ) ...

We have discovered a formula similar to this (but slightly more involved) for

each of the following numbers:

• exp [ 2 G / (pi) ] (where G denotes the Catalan's constant), and

• exp [ 7 zeta (3) / (pi)^2 ].

In the course we stumbled across a new analytic function along with its

concrete integral representation (which is well-defined as a function over

the entire complex plane), which we think is noteworthy. I recently gave a

(half-expository) talk on this subject here at KU:

• Abstract of my seminar talk (September 12, 2014).

• Abstract of my seminar talk (May 1, 2014).

Another paper on this subject is coming out very soon. In addition, we are

simultaneously working on a different subject at the crossroads of Algebraic

Geometry and Number Theory.

[Teaching Activities]

Most research mathematicians (like myself) are affiliated with universities as

professors (KU in my case), and we share our teaching roles. Below is the

list of course(s) (with course webpages) I am currently teaching as well as

courses that I have recently taught:

• [9] Fall 2017

(August 21-Deember 15, 2017)

Math 290 (Elementary Linear Algebra) ,

MonWed 3:00 - 3:50pm, Snow 120

Math 660 (Geometry I)

MonWedFri 2:00 - 2:50pm, Snow 454

• [8] Summer 2017

(June 6-July 28, 2017)

Math 116 (Calculus II) ,

MonTueWedThuFri 10:20 - 11:20am, Snow 306

• [7] Spring 2017

(January 17-May 12, 2017)

Math 290 (Elementary Linear Algebra) ,

TueThu 9:00 - 9:50am, Snow 306

• [6] Fall 2016

(August 23-December 16, 2016)

Math 290 (Elementary Linear Algebra) ,

TueThu 11:00 - 11:50am, Malott 2074

Math 559 (Modern Geometry) ,

TueThu 9:30 - 10:45am, Snow 301

• [5] Summer 2016

(June 7-July 29, 2016)

Math 116 (Calculus II) ,

MonTueWedThuFri 10:20 - 11:20am, Snow 152

• [4] Spring 2016

(January 19-May 12, 2016)

Math 590 (Linear Algebra) ,

TueThu 2:30 - 3:45pm, Snow 454

Math 661 (Geometry II) ,

TueThu 4:00 - 5:15pm, Snow 454

• [3] Fall 2015

(August 24-December 18, 2015)

Math 660 (Geometry I) ,

MonWed 3:00 - 4:15pm, Snow 301

• [2] Summer 2015

(June9-July 30, 2015)

Math 116 (Calculus II) ,

MonTueWedThuFri 10:20 - 11:20am, Snow 301

• [1] Spring 2015

(January 21-May 15, 2015)

Math 105 (Topics in Mathematics) ,

MonWedFri 1:00 - 1:50pm, Budig 120

[Co-organizing an AMS special session]

Professor Purnaprajna , Professor Sane and I served as co-organizers of

• Special session on Algebraic Geometry, AMS Lawrence, KS Meeting (March, 2012).

• Professor John Iskra (Emory & Henry College, VA).

He gave a talk at Algebra Seminar.

• Title: "The notion of smoothness in Algebra, resolution of singularities,

and Zariski category"

Professor Iskra's Abstract (November 30, 2006).

[Co-organizing a conference, co-editing the proceedings]

Professor Tzermias (aforementioned), Professor S.B. Mulay (UT) and I served as co-organizers of a

conference held at UT Mathematics Department in 2002. We had

• Professor Yujiro Kawamata (University of Tokyo, Japan),

and

• Professor Yasutaka Ihara (RIMS, Kyoto University, Japan)

as the keynote speakers.

(see [13] in at the top of this page).

Special thanks to Professor Katz . Last Updated: 10:00AM, 07/11/2018