🧠 Season 2 · Episode 3 is live!
What really lies behind formulas involving the zeros of ζ(s)? In this episode, we slow things down and unpack symmetry, convergence, and the functional equation—showing why certain identities aren’t formal tricks, but inevitable consequences of the analytic structure itself.
No steps skipped. No magic. Just clarity.
#Math #AnalyticNumberTheory #RiemannZeta #ComplexAnalysis #MathTalks
https://cortexdrifter.blogspot.com/2026/03/a-small-taste-from-my-new-book-season-2_8.html

It's good to see my friends Mei-Chi S. ☘️ and Charles S. have published a new book! I am looking forward to reading it!
https://link.springer.com/book/10.1007/978-3-031-93642-5
#SpringerNature #ComplexAnalysis

A tiny typo. A collapsing product.
In Season 2 · Episode 2, we see how entire functions fail when canonical products are mishandled—and why Hadamard’s theorem demands respect.
Mathematics doesn’t forgive shortcuts.
https://cortexdrifter.blogspot.com/2026/03/a-small-taste-from-my-new-book-season-2.html
#ComplexAnalysis #EntireFunctions #Math

🚀 New on the blog!
Season 2 of “A Small Taste from My New Book” kicks off with a deep dive into infinite products, entire functions, and the hidden architecture of complex analysis. If you love math that connects theory with hands-on exercises, this one’s for you!
Read more and challenge yourself:
🔗 https://cortexdrifter.blogspot.com/2026/02/a-small-taste-from-my-new-book-season-2.html
#math #complexanalysis #infiniteproducts #riemannhypothesis

I just got this email regarding the spring 2026 Midwest Several Complex Variables conference:

"Unfortunately we did not get the NSF grant so the conference will not run this year."

I was not planning to attend this time (Florida Polytechnic being, for me, in an inconvenient corner of the "midwest") but I do co-organize a smaller annual workshop with a similar type of NSF conference grant.  We got some funding in 2025 (>insert Theoden meme<), but I am not sure we will try for 2026. This #NSFfunded SCV event getting canceled is not good for anybody.
#NSF #ComplexAnalysis

Curious how a simple mapping can transform circles into vertical lines or pencils of parallel lines into circles through the origin? Discover the elegant interplay between formulas and geometric intuition—and see why Möbius transformations are central to modern mathematics.

#ComplexAnalysis #Math #Geometry #MöbiusTransformation #RiemannHypothesis

https://cortexdrifter.blogspot.com/2026/01/a-small-taste-from-my-new-book-episode-9.html

Episode 5 of “A Small Taste from My New Book” is out!
Explore the beauty of asymptotic analysis, Laplace integrals, and contour integration.
https://cortexdrifter.blogspot.com/2025/12/a-small-taste-from-my-new-book-episode-5.html
If you’re passionate about deep mathematical understanding, check out my books:
📘 The Riemann Hypothesis Revealed
📗 The Essential Transform Toolkit
Both are available on Amazon and written to make advanced concepts accessible and rigorous.
Let’s keep the conversation going, what’s your favorite contour trick?
#Mathematics #ComplexAnalysis #Laplace #Asymptotics #MathBooks #AcademicMastodon

A month to go

I’ve been a bit preoccupied these recent weeks so it was with a shock that I realised that we’re into Week 9, which means just four weeks (including this one) until the end of term and just a month before Christmas. Teaching finishes here in Maynooth on Friday 19th December, but I don’t have any lectures on Fridays so in my case it will finish the day before (with a tutorial). I don’t know how many students will be there, but the module concerned is my 4th year Mathematical Physics module and the students are very hard-working, so I think most will attend. After such a busy term I’m sure that they will need a break as much as I will.

I had to rejig the schedule for both modules I am teaching this semester to accommodate the introduction of in-class tests to replace take-home assignments (for reasons I outlined here). I’ve also been handing out voluntary exercises for practice, not counting towards the module mark but for formative reasons. Both modules are mathematical in nature, and I think the best way to learn mathematics is by doing it…

Despite the changes with respect to last year, I am still roughly on track. In my Engineering Mathematics module I’ve just finished Laplace transforms, and will start Fourier methods tomorrow. With the mathematical physicists, I am in the middle of complex analysis, having done complex differentiation and conformal mappings and starting complex integration next week.

I still have a couple more class tests to get through. On the positive side, the students are turning up for them and have expressed approval for the fact that they don’t have compulsory homework to do off-campus. This form of assessment is undoubtedly harder work for the students, it’s also better preparation for the examination that take-home assignments.

We’ve just received the draft examination timetable for January, and I’m pleased that both of the examinations for which I am responsible will take place quite early in the examination period (on 12th and 15th January, respectively) so I should be able to get them corrected in time to have a break for some research before teaching resumes at the start of February.

#complexAnalysis #engineeringMathematics #genai #generativeAi #mathematics #maynoothUniversity

I’ve just published a new post exploring the hidden oscillations behind prime numbers, focusing on the Mertens function, Möbius sums, and their deep ties to the Riemann Hypothesis.
If you’re into analytic number theory or curious about the “structure inside the chaos” of primes, you might enjoy this one.
https://cortexdrifter.blogspot.com/2025/11/the-hidden-oscillations-behind-prime.html
#math #numbertheory #primes #riemannhypothesis #complexanalysis

My photos from the Oct. 10-12 Midwestern Workshop on Asymptotic Analysis :gauss: , here at #PurdueFortWayne 🐘
https://www.flickr.com/photos/coffmanadam/albums/72177720329689718
#NSFfunded #math #MathConference #RealAnalysis #ComplexAnalysis

\(1^{st}\) announcement for the 2025 Midwestern Workshop on Asymptotic Analysis - October 10 - 12 at #PurdueFortWayne 🐘 .
Participant registration is now open (through Sept. 21 to be considered for travel support), follow the instructions on the web site:
http://mwaa.math.indianapolis.iu.edu/
#NSFfunded
#MathConference #ComplexAnalysis #RealAnalysis #Indiana

\(0^{th}\) announcement for the 2025 Midwestern Workshop on Asymptotic Analysis - October 10 - 12 at #PurdueFortWayne 🐘 .
The web site has a preliminary list of 2025 speakers including our keynote speaker Alexandre Sukhov 🇫🇷 . Online registration and the request form for travel support will be available soon on the web site:
http://mwaa.math.indianapolis.iu.edu/
Students are encouraged to display a poster!
#NSFfunded
#MathConference #ComplexAnalysis #RealAnalysis #Indiana

The #math department at #PurdueFortWayne 🐘 welcomes two new tenure-track faculty!
Vahan Mkrtchyan's research is in #GraphTheory and theoretical computer science :k33: :k5:
Liding Yao's research is in #ComplexAnalysis and geometric analysis

My "short communication" has been accepted for #ICM2026 ! The topic is in analysis but I just got the acceptance email and don't have any scheduling or other information yet. The long communication speakers are listed on the web site:
https://www.icm2026.org/event/ac193975-5d24-4628-8c30-ddb23de19a8b/home
Under other circumstances 🤦‍♂️ I would invite everyone to my talk!
#Math #MathConference #ComplexAnalysis

Made a new #complex #function #visualizer using #Shadertoy #GLSL

It creates more lines in regions with a lower gradient/derivative, which feels like a grid with repeating steps/lines. Functions can be explored much better in my opinion.

Link: https://www.shadertoy.com/view/tXc3Ws

#ComplexAnalysis #DomainColoring #Math #CreativeCoding

\(f(z)=\frac{z^{10}-a}{z^{12}+\frac{z}{a}}\)

with \(a\) on the unit circle.

Perfect loop

#Animation #Math #Mathematics #Mathart #Complex #ComplexAnalysis #ComplexPlane #GLSL #Shadertoy #PerfectLoop

Sort of \(f(z)=\frac{(z^2-1)(z-2-i)^2}{z^2+2+2i}\)

Shadertoy: https://www.shadertoy.com/view/wcyGRw

#Animation #Math #Mathematics #Mathart #Complex #ComplexAnalysis #ComplexPlane #GLSL #Shadertoy

Our #PurdueFortWayne 🐘 #math department colloquium talks this semester, on #RealAnalysis #ComplexAnalysis #GraphTheory
https://photos.app.goo.gl/tQaqPeZXf3nMHKzP9

My colleagues and I have started the process of applying for a grant from #NSF. This is a strange time for such things here ( 🇺🇸 ) but if anyone is interested I can "live-blog" the process here to document any surprises or changes from our past experience. Specifically we are applying for a "conference grant" to support travel for graduate students and postdocs to an annual regional conference series on mathematical analysis. The conference organizers, including myself, have successfully applied for this grant approximately every year since 2015 - last year it was at Indiana University in Bloomington and for 2025 the location will rotate here to #PurdueFortWayne. So - stay tuned, either for good news or an informative fail-in-public anecdote!
#NSFfunded #math #MathConference #RealAnalysis #ComplexAnalysis

Amid all the excitement last week I forgot that it was the sixth teaching week of the Semester. That means that we’re now past the halfway point. Among other things that meant that examination papers were due in on Friday (8th November). That means two papers for each module I’m teaching, one to be sat in January and another for the repeat opportunity in August, so that’s four altogether.

I always find setting examination questions very difficult. In theoretical physics we want to stretch the stronger candidates at the same time as allowing the weaker ones to show what they can do. It’s a perennial problem how to make the questions neither too easy nor too difficult, but it is compounded this time by the fact that I’m teaching two modules for the very first time so judging the right level is tricky.

Another issue is that I’m once again in a situation in which I have to set examination papers without having taught all the material. At least I’ve covered the first half of the content so I have some idea of what the students found difficult, but that’s not the case for the second half. It should be a bit easier next year once I’ve experience of covering the whole syllabus. Assuming, of course, that I’m teaching the same modules again next year, which is by no means guaranteed…

I’m teaching a module on Differential Equations and Complex Analysis for 4th year students and just about ready to switch to the part that comes after the and. I taught a bit of Complex Analysis when I was at Sussex and I’m quite looking forward to it, although it does pose a particular challenge. Some of the class are doing a Double Major in Theoretical Physics and Mathematics, and have done quite a lot of Complex Analysis before, while others are doing a Single Major in Theoretical Physics and haven’t really done any. I have to somehow find a way to satisfy these two different groups. The only way I can think of to do that is to teach the subject as a physicist rather than a pure mathematician, with an emphasis on examples and real-world applications rather than in the abstract. We’ll see how this works out over the next few weeks.

P.S. On the subject of Complex Analysis, I just remembered this post from a few years ago.

https://telescoper.blog/2024/11/11/midpoint/

#ComplexAnalysis #education #ExaminationQuestions #Examinations #mathematics