# Algebra and lattices in Hawaii 2018

Pictured: Pondering the smallest lattice not yet known to be a congruence lattice of any finite algebra.

Three Legends of Universal Algebra and Lattice Theory,

worked most of their careers at the University of Hawai’i at Manoa.

They all will be approximately 70 years old in May 2018, and a conference, ALH-2018, was organized by PhD alumnus William DeMeo and others to celebrate their achievements.

# 1994 result of Smith and Csordas inspires solution to Newman’s Conjecture

Wayne Smith with Varga and our professor emeritus George Csordas in a 1994 paper gave results on the de Bruijn-Newman constant $\Lambda$, where the statement $$\Lambda\le 0$$ is equivalent to the Riemann Hypothesis (some of Riemann’s notes on this shown above). Now in 2018 Terence Tao and Rodgers have shown $$\Lambda\ge 0.$$ Their primary inspiration, judging from the abstract, was Smith et al.’s work:

For each $t \in {\bf R}$, define the entire function $$H_t(x) := \int_0^\infty e^{tu^2} \Phi(u) \cos(xu)\ du$$ where $\Phi$ is the super-exponentially decaying function $$\Phi(u) := \sum_{n=1}^\infty (2\pi^2 n^4 e^{9u} – 3\pi n^2 e^{5u} ) \exp(-\pi n^2 e^{4u} ).$$ Newman showed that there exists a finite constant $\Lambda$ (the de Bruijn-Newman constant) such that the zeroes of $H_t$ are all real precisely when $t \geq \Lambda$. The Riemann hypothesis is the equivalent to the assertion $\Lambda \leq 0$, and Newman conjectured the complementary bound $\Lambda \geq 0$.
In this paper we establish Newman’s conjecture. The argument proceeds by assuming for contradiction that $\Lambda < 0$, and then analyzing the dynamics of zeroes of $H_t$ (building on the work of Csordas, Smith, and Varga) to obtain increasingly strong control on the zeroes of $H_t$ in the range $\Lambda< t \leq 0$, until one establishes that the zeroes of $H_0$ are in local equilibrium, in the sense that locally behave (on average) as if they were equally spaced in an arithmetic progression, with gaps staying close to the global average gap size. But this latter claim is inconsistent with the known results about the local distribution of zeroes of the Riemann zeta function, such as the pair correlation estimates of Montgomery.

# AMS Meeting #1147

(The following information is adapted from information about our 2012 Western Sectional meeting.)

#### Equipment for speakers

The equipment available for speakers at this meeting is a computer, a computer projector, and either blackboards or whiteboards. There are no traditional overhead projectors that use acetate sheets.

Speakers using computer projection can use their own laptops, but, for smoother transitions between talks, our hosts recommend using the provided computer or connecting one laptop to the projector (yours or one volunteered from within your speaker set) and have speakers bring their talks on thumb drives. The projector comes with a standard VGA cable; anyone using a mac must bring the appropriate adaptor.

#### Interactive Map

View AMS Meeting March 3-4 2012 in a larger map

This is projected to be the largest meeting of the Western Section of the AMS ever, with over 500 participants.

There will be 4 plenary lecturers and 25 special sessions. The special sessions are distributed as follows:

1. 10 in the Business School,
2. 7 in Kuykendall,
3. 4 in Webster,
4. 2 in POST,
5. 1 in Keller Hall,
6. 1 in Miller Hall.

The specific sessions can be located on the map by clicking on a colored marker. The walk between Business (where many Analysis sessions are held) and Kuykendall (where many Algebra sessions are held) is about 0.3 miles, and is indicated on the map.

#### Lunch Options

The Campus facilities are closed during weekends, however a lunch wagon serving Indian dishes agreed to open from 11 am to 2 pm. The "India Cafe" outlet is operating at Varsity Circle that is centrally located on the Manoa Campus. This will be by far the most convenient place to have lunch during the meeting and they are prepared to offer up to 200 meals.

South Indian Chicken Curry - Juicy chicken stir-fried with onions, garlic, ginger, curry leaves, anise star, cardamom, cinnamon sticks and cloves then slow cooked in a medium spiced red curry sauce.
Chicken Tikka Masala - Boneless chicken marinated in yogurt, lemon juice and herbs then slow cooked in a sweet tomato and cream curry sauce.
Spicy Seafood Curry
Vegetarian Plate - Curried Mix Vegetables and Chana masala (chick peas) served with rice.

There are two other possibilities involving some walking.

There are several restaurants at the intersection of University Avenue, Beretania and King Street. It will take 15 to 20 minutes to walk there.

A little further away, but with a larger offering is the Manoa Market Place. There is a shortcut through the mountain side of the Campus that will take you to the Manoa Market Place in 20 to 25 minutes. There are Korean, Japanese, Italian restaurants and fast food outlets of various persuasions.

While buses run to these places from the UH, it would be hopeless during the weekend when buses are on special reduced schedules.

A much longer trip is required to the Ala Moana Shopping Center that contains a large food court and numerous other restaurants. There is a bus connection (#6) but this would be very time consuming. Taking a cab might be reasonable for a group that wishes to lunch together.

Please see our Travel page for information about parking, getting to campus from your hotel, and beaches.

# Visiting UH Manoa Mathematics

The following information is adapted from a post from 2011.

#### Parking at UH

On Saturday people can park anywhere on campus for a flat fee of 5 dollars. On Sunday parking is free. However, renting a car for driving to the UH is not worth it. Parking in Waikiki is expensive and it is easy to get from Waikiki to the UH campus by bus or cab.

#### TheBus (thebus.org)

The bus fare for a single trip (any distance) plus one transfer is 2.50 dollars exact change. For seniors over 65 with a Medicare card the rate is 1 dollar.

The #4 bus runs from Kuhio Avenue to the University. Persons staying at Hokele Suites get to Kuhio Avenue in a few steps heading toward the sea (makai). People staying in the Maile Sky Court only need to look for the nearest bus stop. To get to the UH take the bus on the mountain (mauka) side of Kuhio Avenue.

View Larger Map

People staying at the Hawaii Prince Hotel or the Hilton Hawaiian Village will have to walk 5 to 10 minutes to the #4 bus stop on the McCully Bridge over the Ala Wai Canal or take the very frequent #8 bus to the Ala Moana Shopping Center and there catch the #6 bus.

View AMS Meeting March 3-4 2012 in a larger map

The #4 bus runs along Kuhio Ave and departs at Monsarrat/Kalakaua on Saturday at 6:00a, 6:30a, 6:58a, 7:25a, 8:15a. On Sunday departure times are 6:15a, 6:55a, 7:30a, 8:00a, 8:30a. It takes about 25 minutes to reach the UH. Monsarrat/Kalakaua is located at the Diamond Head end of Waikiki so it will take some 5 to 10 minutes for the bus to reach the other end of Kuhio Ave.

On Saturday the A City Express Bus leaves from the Ala Wai Community Park at 5:55a, 6:25a, 6:35a, 6:55a, 7:05a, 7:25a and on Sunday at 6:20a, 6:50a, 7:20a and 7:50a. The bus stop is on Kapiolani Boulevard Diamond Head of McCully Street (turn right after crossing McCully bridge coming from Waikiki). This bus takes 9 minutes to get to the UH.

The #6 bus leaves the Ala Moana Shopping Center, Kona Street (direction Woodlawn) on Saturday at 5:42a, 6:07a, 6:37a, 7:04a, 7:34a, 8:04a, 8:35a and on Sunday at 6:21a, 7:06a, 7:54a, 8:24a reaching the UH in about 10 minutes.

#### Cabs

Cabs in Hawaii have to be pre-ordered by phone. The fare from Waikiki to the UH is 11 to 16 dollars depending on location in Waikiki. Thus sharing a cab between three or four people would be a reasonable option.

#### Beaches

The Hilton Hawaiian Village is fronting a swimming beach. The Hawaiian Prince Hotel overlooks the yacht harbor but a short walk is required to get to a swimming beach. From the Hokele Suites and the Maile Sky Court one can reach the busy Waikiki Beach in a few minutes.

#### Math department's campus location

Floor   Keller Hall Physical Science Building
5 Math faculty office
4 Math administration and faculty offices   Math faculty offices
3 Math faculty offices Math faculty offices; Geography
2 ICS NASA astrobiology center; Study abroad
1 ICS International Students and Scholars; Physics