Yasuyuki Kachi
[photo] Department of Mathematics
University of Kansas
Lawrence, KS 66045

OFFICE: Snow Hall 622

PHONE: (785) 864-7308
FAX:   (785) 864-5255 

EMAIL: kachi@ku.edu

MATHEMATICS DEPARTMENT : www.math.ku.edu




  • [My Specialty]
    Right off the bat: Number theory is my research specialty. More specifically, my research encompasses the following two
    well-defined facets ("sub-disciplines") of number theory:
      • analytic number theory (theory of zeta functions), and
      • Gauss-Jacobi sums.
    Some follow-up explanation on the taxonomy of sub-disciplines of number theory, à la AMS (= American Mathematical
    Society), is found in pages 3–4 of my notes "Sample Lecture Notes, November 2019" (four paragraphs down, just
    scroll down a bit, thank you).

  • [My recent paper]
    Just to give you an idea, here is a joint research paper I have recently co-authored. Feel free to take a peek and browse:
    • Y. Kachi and P. Tzermias,
            [Note: This came out in March, 2019 whereas the journal goes by Japanese Fiscal Years.]
  • More information on my publications below.

  • [Please ignore this section if you are a mathematician]
    I know, right? Admittedly, the paper is inundated with jargons that only experts can understand. That actually gives you some
    wouldn't dare think twice when it comes to this — or in less palatable terms, people are generally presumptuous about what
    we do — not that that's anybody's fault, no finger-pointing game. To cut to the chase:
  • Me and my colleagues here at KU are a legion of experts with missions that require some intelligence, enough to add some
    new wrinkles to the game of updating the collective pre-existing scientific knowledge of the humankind 24/7/365.
  • Too pompous/self-assertive? (I saw this coming..) No, not so fast, take a deep breath — no bragging rights. Relax. The sole
    and the most important point I'm trying to make here is: The highest level of math is still in the works. You still probably
    won't buy it unless I elaborate what that means. So, read this (if you feel like it and indeed have a stomach for it):
  • All right, so I said 'presumptuous'. 'Presumptuous' as in people generally assume that all of us faculty at KU Math "teach
    full-time". Is that true? The answer is, some of us do teach full-time, but the most of us, including myself, do research-and-teaching.
    So I myself do teach as well (which was actually hinted at by the above link to my class notes, lol..). While some KU students
    prefer to have someone who is a full-time teaching staff as their instructor, and they give good reasons, I say there are viable and
    tenable counterarguments, such as one tendered by Professor Henry Rosovsky, a former Dean of Arts & Sciences at Harvard University,
    in his book "The University — An Owner's Manual" pp. 86–98 "Why Would an Undergraduate Want a Research-Oriented Teacher?"

  • [My teaching]
    below are some (more or less randomly selected) lecture notes. I define those lecutre notes as the hallmarks of my teaching:

  • [Back to my Research: Papers]
  • In preparation:
    • C. Fang, L. Grand, Y. Kachi and P. Tzermias: "Sum Formula on Multi-zeta Values After Hoffman–Granville–Zagier–Ohno and
                        Akiyama–Tanigawa Polynomials", In preparation.
  • Preprints:
  • Selected publications (in number theory):
                Tsukuba Journal of Mathematics Vol. 42, No. 2 (2018), 309–334.
    • Y. Kachi and P. Tzermias: "On the m-ary partition numbers", Algebra and Discrete Mathematics, Vol. 19 (2015), No. 1, pp. 67–76.
    • Y. Kachi and P. Tzermias: " Infinite Products Involving ζ(3) and Catalan's Constant", Journal of Integer Sequences, Vol. 15 (2012),
                Article 12.9.4. (16pp.)
  • My research history overview (narrative) is found down below.

  • [More on my Research — Research History Overview]
    In the above I said number theory is my specialty. Now I must spit it out: As a student, I studied algebraic geometry. I started out my career as
    an algebraic geometer. I used to publish algebraic geometry papers. Then midway through my career I shifted gears. Now I consider myself as
    a full-blown number theorist. I would like to share my odyssey, how I eventually resettled in a new home. First thing first, here are my selected
    algebraic geometry publications (they are all before the transition/conversion):
  • Selected publications (in algebraic geometry):
    • Y. Kachi "Global Smoothings of Degenerate Del Pezzo Surfaces with Normal Crossings", Journal of Algebra 307 (2007), 249–253.
    • Y. Kachi and E. Sato "Segre's Reflexivity and an Inductive Characterization of Hyperquadrics", Memoirs of AMS, Number 763 (2002), 116pp.
        [Note: Publishing a paper in Memoirs of AMS is usually counted as equivalent to publishing a book.]
    • Y. Kachi and J. Kollár "Characterization of Pn in arbitrary characteristic", Asian Journal of Mathematics, 4, No. 1 (Special Volume
                  in Memory of K. Kodaira) (2000), 115-122.
    • Y. Kachi "Flips from 4-folds with isolated complete intersection singularities", American Journal of Mathematics, 120 (1998), 43–102.
  • So here's my narrative, voilà:
              [ Still writing up this paragraph, duh..]

  • [Graduate Student Advising]
    Graduate student advising is an integral part of my work. It is inseparably linked with research. At its core, it is about siring my next
    generation counterparts. By nature, one-on-one session with graduate students is very different from teaching an (undergraduate) class
    (populated by non-math-track students). Capstone of working with graduate students is putting heads together, racking our brains, and
    churning out ideas, in a bid to amass original results (theorems), and also giving the lowdown on writing up theses, the publication process
    (from submissions, to effective communication with the editorial office), impactful presentations, etc. In a nutshell, my job is to upskill
    them how to fare well in their subsequent research career. I also teach graduate courses in a class-setting from time to time, ranging from
    the entry-level to an advanced level.
  • Currently, I advise two graduate students
  • In the past, I have advised one graduate student
        • Chengzhen Fang (received M.A. in 2016)
  • Lucian Grand research synopsis:
    Lucian Grand is a third-year Ph.D.-track student. Lucian did his undergraduate at Haverford College in Haverford, PA, where he studied
    Waring's problem. Lucian is currently enrolled at KU as a graduate student since 2017, seeking his Ph.D. in math. I took Lucian
    under my wing in September, 2018. Ever since Lucian and I work together side-by-side on the subject of the Riemann-Hurwitz
    ζ-function. Lucian's acquired and bequeathed knowledge and acumen quickly proved to be serviceable. Lucian's contribution thus far
    includes: new recursion algorithms to generate well-known polynomial sequences by way of beefing up "umbral calculus", and
    convergence of a series that gives a new analytic continuation of the Riemann zeta ζ(s). These are original work, albeit they were
    crystallized while under my supervision. Lucian plans to incorporate these as a part of his Ph.D. thesis. What's more: Lucian's results
    have a broader impact enough to have direct bearings on the crucial part of my on-going joint research with my permanent collaborator
    Pavlos Tzermias (professor at University of Patras, Greece); and Chengzhen Fang (my former graduate student, currently at KU Economics
    working towards his Ph.D.). Naturally, I invited Lucian to become the fourth co-author of our joint paper. [ We are still drafting that paper
    as we speak so I have to keep it vague about his work for now, but the paper will be out soon. ] Recently (in December, 2019) Lucian
    gave a talk (a talk open to all who wish to attend), as per KU's requirement, called "Preliminary Exam", an exam required for every
    Ph.D.-track student to pass in order to stay in the Ph.D. program. Lucian delivered a précis of his work. Outcome? Lucian still hangs on to
    the program, which he wouldn't had he failed, so... take a guess. Overall Lucian is on the right-track, and I am cautiously optimistic about
    the prospect of more production coming from him.
  • Conner Emberlin research synopsis:
    Conner Emberlin is a third-year Master-track student. Conner did his undergraduate at KU, majored in math. As an undergrad Conner did
    some exploratory research with me (in Spring 2017), in part to "test the water". While that being on the go the prospect of continuing to work
    with me grew in him. That vision was materialized shortly thereafter, namely, Conner got accepted into our math Master's program in summer,
    2017, just as he graduated from KU with Bachelor's degree. Ever since Conner and I work together side-by-side. Conner's main interest is
    sums of roots of unity (Gauss–Jacobi sums), with a loftier goal in mind, which is to cast light on the theory of L-functions (functional identities).
    Conner's mathematical prowess was on display when he saw Galois groups looming behind the scenes in the context where they are hardly
    perceptible. And he didn't stop there — Conner capitalized that observation and conceived a novel idea to refurbish the foundations of the theory
    he was flirting with from complete scratch, incorporating the perspective of group representations. Though these developments took
    place under my oversight, in my discernment they are original, imaginative, and at the same time downright viable postulations (working
    hypotheses), to the extent it is highly likely they will evolve into a heap of compelling results of a publishable quality. Now Conner is in the
    phase of preparing for his Master's Defense, which will happen in May this year (May, 2020). Conner and I are currently fervently working
    towards getting a hold of decisive, substantial results. Then drafting a joint paper will ensue. [ Again, the paper-drafting process still under
    way is the reason why I have to use vague terms about this work, at least for the time being.]

  • [Service]
    At universities, in addition to research and teaching, we, faculty members, are tasked with meeting diversiform demands. They are
    collectively termed as "service". So, what exactly do we do here? Let me walk you through it.
  • Before getting into it, laying a stress on the following never hurts: Paying heed to l'esprit de corps is paramount. Service is more often
    than not a team work, so it comes with a greater responsibility than an individual work, to the extent that a failure/bungled delivery on
    your part can be detrimental to your colleagues' and your institution's well-being. (As cliché as this sounds, I really mean it.)
  • In my case, when it comes to fulfilling service roles, I always proactively communicate with the administration of my work unit
    necessary resources, and seek timely advice, whenever necessary/applicable.
  • So, let's get a glimpse of our service duties: I will take my own case as an example. At my work unit (KU Mathematics Department),
    I'm routinely assigned to work as a member of various committees (below are the committees that I had actually served on, over a
    protracted period of time between 2005–2020):
          • Preliminary Exam for Ph.D.(aforementioned),
          • Master's Defense Committee (aforementioned),
          • Hiring Committee (Assistant Professor Position),
          • KU Math Prize Competition Committee (Problem Writing/Proctoring/Grading),
          • Center for Teaching Excellence Liaison Committee,
          • Library Committee,
          • Undergraduate Committee,
          • Graduate Qualifying Exam (Problem Writing/Proctoring/Grading).
  • In addition, participating in faculty meetings, including casting my votes on motions, etc. is also deemed as a part of the service roles.
  • Well, if you think that's all, you are dead wrong.. Service extends beyond the confines of on-campus duties. Let's take a look.
  • [Refereeing]
    Refereeing job for peer-reviewed journals is a super-important scholarly service. Most importantly, this job is gratis. Like my peers,
  • [Organizing Meetings]
    And my list goes on. Organizing academic conventions (meetings, conferences) is yet another important job, also classified
    as "service". I am always eager to seize opportunities to act in an organizational capacity at conventions to demonstrate my organizing
    skills and initiative. Well, that said, such opportunities don't just come around. I was fortunate enough to have done it twice in the past.
  • [My Pledge]
    I always try to promote collegiality (which includes sustaining and nurturing my own). I pledge to continue to be an accessible, resourceful,
    and serviceable member of the KU community. I am full of determination enough to always try to be heartfelt and professional in executing
    an array of services at KU and in the academic community at large.

Still Under Construction.. More to come soon.

    Last Updated: 3:25PM, 02/18/2020