Yasuyuki Kachi
Department of Mathematics
University of Kansas
Lawrence, KS 66045
OFFICE: Snow Hall 622
PHONE: (785) 8647308
FAX: (785) 8645255
EMAIL: kachi@ku.edu MATHEMATICS DEPARTMENT : www.math.ku.edu
[Professor Kachi's Graduate Student Advising]
[Professor Kachi's Curriculum Vita]
[Professor Kachi's Recent talks]
1. Colloquium (December 3, 2015),
 Title: Primes, zeta and asymptotic formulas
 GranvilleZagier's multi zeta values
1. Colloquium at University of Missouri at Kansas City (November 13, 2015),
2. Zeta Institute Weekly Seminar at
Tokyo Institute of Technology (May 26, 2014),
[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 mary partition numbers", Algebra and Discrete Mathematics,
Vol. 19 (2015), No. 1, pp. 6776.
 [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), 249253.
 [5] Y. Kachi and S.B. Mulay:
"LocaltoGlobal Correspondence in Algebraic Geometry",
Proceedings of Fano Conference (A. Conte,
A. Collino, M. Marchisio, ed.) 2004, pp. 485514.
 [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), 115122.
 [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. 155165.
 [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), 350390.
 [10] Y. Kachi:
"Flips from 4folds with isolated complete intersection
singularities",
American Journal of Mathematics, 120 (1998), 43102.
 [11] Y. Kachi: "Flips of semistable 4folds whose degenerate fibers are
union of Cartier divisors which are terminal factorial 3folds",
Mathematische Annalen, Vol. 307 (1997), 647662.
 [12] Y. Kachi: "Extremal contractions from 4dimensional manifolds to
3folds",
Annali della Scuola Normale Superiore di Pisa, Serie IV,
XXIV, 1 (1997), 63131.
[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.)
 F. Campana and Q. Zhang, Compact Kaehler threefolds of (pi)_1general
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 nonisotriviality 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 ArtinSchreier curves;
 K. Schwede, Gluing schemes and a scheme without closed points.
[Joint Seminars]
I often do a joint seminar with
when a talk scheduled in either their or my seminar potentially attracts
a broader audience.
[Professor Kachi's Brief profile]
I am a research mathematician (just like any other colleagues of mine in KU
Mathematics Department).
I specialize in
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
 Professor Pavlos Tzermias at
In our recent joint publication ([1] in the above list), he and I have proved new
Wallistype
infinite product formulas for some numbers involving two famous constants,
namely, the Catalan's constant and the Apery's constant (the latter is also
Here, the original Wallis infinite product formula (classical) states
(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 ].
He and I are currently developing a new theory on analytic continuations.
In the course we stumbled across a new analytic function along with its
concrete integral representation (which is welldefined as a function over
the entire complex plane), which we think is noteworthy. I recently gave a
(halfexpository) talk on this subject here at KU:
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:
(August 21Deember 15, 2017)
MonWed 3:00  3:50pm, Snow 120
MonWedFri 2:00  2:50pm, Snow 454
MonTueWedThuFri 10:20  11:20am, Snow 306
(January 17May 12, 2017)
 Math 290 (Elementary Linear Algebra) ,
TueThu 9:00  9:50am, Snow 306
(August 23December 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
MonTueWedThuFri 10:20  11:20am, Snow 152
(January 19May 12, 2016)
TueThu 2:30  3:45pm, Snow 454
TueThu 4:00  5:15pm, Snow 454
(August 24December 18, 2015)
MonWed 3:00  4:15pm, Snow 301
MonTueWedThuFri 10:20  11:20am, Snow 301
(January 21May 15, 2015)
MonWedFri 1:00  1:50pm, Budig 120
[Coorganizing an AMS special session]
[Hosting Visitors]
He gave a talk at Algebra Seminar.
 Title: "The notion of smoothness in Algebra, resolution of singularities,
[Coorganizing a conference, coediting the proceedings]

Professor Yasutaka Ihara (RIMS, Kyoto University, Japan)
We (the three of us) served as coeditors of
the proceedings "Recent Progress in Arithmetic and Algebraic
Geometry"
(see [13] in at the top of this page).