Podcast appearances and mentions of Richard Weiss

S1E10: Host Anthony Murray, Chief Interoperability Officer, interviews MRO Chief Information Security Officer, Richard Weiss. They discuss all things cybersecurity as Cybersecurity Month wraps up at the end of October. Find all of our network podcasts on your favorite podcast platforms and be sure to subscribe and like us. Learn more at www.healthcarenowradio.com/listen

Nicht nur «auf den Hund», sogar «auf die Katze» gekommen. Mit: Reinhard Papula (Erzähler), Wolfgang Schön (Richard Weiss), Margarethe Hamm (Katze) Tontechnik: Andy Mettler Regie: Rainer Zur Linde Produktion: SRF 1985 Dauer: 07:33

Ingest High level Cat 16 topicx references men Blood Brothers wtf is happenin' ? https://youtu.be/uzWcC_s3nkI Vic Flair Ruste Juxx https://youtu.be/A5k28lBcHU8 My dawg on Chris Hardicks show https://youtu.be/7unyDYKgap0 Support patreon.com/Firecrotch Original Whiggaz Live youtube.com/focuscds Whiggaz Patreon.com/whiggaz Greetings, comedy lovers! If you're seeking an out-of-this-world experience that will keep you laughing, you'll want to beam yourself down to Sixth Street in downtown Austin, Texas. The Comedy Mothership, located in the historic Ritz Theater, has finally landed, and it's ready to take you on a hilarious journey you won't soon forget. The Comedy Mothership is the brainchild of none other than the famous comedian and number one podcaster, Joe Rogan. Having taken over the Ritz Theater in 2022, Rogan's goal was to provide a comedy community that would draw comics from all around the world, right here in Austin. After a year of renovations led by local architect Richard Weiss, the Comedy Mothership is now open and ready to make you laugh until you cry. This comedic gem, situated at 320 E. 6th Street, features two showrooms: Fat Man, the larger headliner showroom, and Little Boy, an intimate space showcasing the best of local and national talent. With cabaret-style seating arrangements and discreet table service, you'll feel right at home as you settle in for a night of laughter. Norman Gene Macdonald[i] (October 17, 1959[ii] – September 14, 2021) was a Canadian stand-up comedian, actor, and writer whose style was characterized by deadpan delivery and the use of folksy, old-fashioned turns of phrase.[1][2][3] He appeared in many films and was a regular guest on late-night talk shows, where he became known for his chaotic, yet understated style of comedy.Many critics and fellow comedians considered him to be the ultimate talk show guest.

Allegheny County lawyer Richard Weiss is the 2022 Pennsylvania Green Party Candidate for U.S. Senate. 

Threshold Radio We Have Dr. J.J. Hurtak, Ph.D., Ph.D., & Dr. Desiree E. Hurtak Ph.D. From The Academy For Future Science, International. Show58 On tonights show we have Dr. J.J. Hurtak, Ph.D., Ph.D., & Dr. Desiree E. Hurtak Ph.D. from The Academy for Future Science, International. We spoke about NASA’s interesting confirmation of “nucleobases” that make up our DNA now acknowledged in meteorites that have landed in Antarctica and Australia. We also discussed Ancient Aliens, Pyramids, Crop Circles and more. Suzanne Taylor talks with us about crop circles and the story of a truly amazing Psychic man from the Netherlands. Suzanne’s amazing movie on The Crop Circle Phenomenon Michael Kleen and his special guest Richard Weiss, owner of The Haunted Bowen building, one of the last standing buildings on the grounds of the old Peoria State Hospital, located in Bartonville, Illinois

On tonights show we have Dr. J.J. Hurtak, Ph.D., Ph.D., & Dr. Desiree E. Hurtak Ph.D. from The Academy for Future Science, International. We spoke about NASA’s interesting confirmation of “nucleobases” that make up our DNA now acknowledged in meteorites that have landed in Antarctica and Australia. We also discussed Ancient Aliens, Pyramids, Crop Circles and more. Suzanne Taylor talks with us about crop circles and the story of a truly amazing Psychic man from the Netherlands.      Suzanne’s amazing movie on The Crop Circle Phenomenon Michael Kleen and his special guest Richard Weiss, owner of The Haunted Bowen building, one of the last standing buildings on the grounds of the old Peoria State Hospital, located in Bartonville, Illinois

It’s the 5th Annual “Roy and Jimmy” Christmas Show! This year’s play is “Christmas Vacation”. They are joined by Claudia Cortez, Amy O’Neill, Robin Williams, Dawn Brewster, Ariana Armada-Casino, Stephanie Brynjolfson, Sean Williams, Donna Maine, Richard Weiss, and the Harbottles, Kathie, Steve, and Emma!

WITF’s Election 2020 coverage on Smart Talk continues Friday with a candidate running for statewide office. Heather Heidelbaugh is a Republican running for Pennsylvania Attorney General. The Pittsburgh-area attorney is on the ballot with incumbent Democrat Josh Shapiro, Libertarian Daniel Wassmer, and Green Party candidate Richard Weiss. Conversations with candidates are designed to give voters … Continue reading "Smart Talk Friday: Heidelbaugh for Attorney General and EPA sued over Pa. not meeting Chesapeake cleanup goals"

In this episode, I have the great pleasure of speaking about all things mindful practice with international cello soloist Alisa Weilerstein. Alisa has attracted widespread attention for her playing that combines natural virtuosity and technical precision with impassioned musicianship.  In this episode, Alisa shares insight on: How her parents nurtured a natural unfolding and healthy progression of her career Practicing: focusing efficient practice, intentional breaks and time off management (so important for long term sustainability + physical and mental health!) Her approach to learning a piece The importance of keeping musicality part of the technical work (as she said “Keeping everything married”) How practicing mindfully is the key for her to get rid of nerves and feel comfortable in performance How she plays mock performance for friends How to develop a natural rubato using the metronome … and much more!   It's an information and inspiration packed episode and I hope you enjoy and find value in our discussion!   MORE ABOUT ALISA WEILERSTEIN alisaweilerstein.com twitter.com/aweilerstein facebook.com/AlisaWeilerstein instagram.com/alisaweilerstein/   Alisa Weilerstein is one of the foremost cellists of our time. Known for her consummate artistry, emotional investment and rare interpretive depth, she was recognized with a MacArthur “genius grant” Fellowship in 2011. Today her career is truly global in scope, taking her to the most prestigious international venues for solo recitals, chamber concerts, and concerto collaborations with all the preeminent conductors and orchestras worldwide. “Weilerstein is a throwback to an earlier age of classical performers: not content merely to serve as a vessel for the composer's wishes, she inhabits a piece fully and turns it to her own ends,” marvels the New York Times. “Weilerstein's cello is her id. She doesn't give the impression that making music involves will at all. She and the cello seem simply to be one and the same,” agrees the Los Angeles Times. As the UK's Telegraph put it, “Weilerstein is truly a phenomenon.”   Bach's six suites for unaccompanied cello figure prominently in Weilerstein's current programming. Over the past two seasons, she has given rapturously received live accounts of the complete set on three continents, with recitals in New York, Washington DC, Boston, Los Angeles, Berkeley and San Diego; at Aspen and Caramoor; in Tokyo, Osaka, Guangzhou, Shenzhen, London, Manchester, Aldeburgh, Paris and Barcelona; and for a full-capacity audience at Hamburg's iconic new Elbphilharmonie. During the global pandemic, she has further cemented her status as one of the suites' leading exponents. Released in April 2020, her Pentatone recording of the complete set became a Billboard bestseller and was named “Album of the Week” by the UK's Sunday Times. As captured in Vox's YouTube series, her insights into Bach's first G-major prelude have been viewed almost 1.5 million times. During the first weeks of the lockdown, she chronicled her developing engagement with the suites on social media, fostering an even closer connection with her online audience by streaming a new movement each day in her innovative #36DaysOfBach project. As the New York Times observed in a dedicated feature, by presenting these more intimate accounts alongside her new studio recording, Weilerstein gave listeners the rare opportunity to learn whether “the pressures of a pandemic [can] change the very sound a musician makes, or help her see a beloved piece in a new way.”   Earlier in the 2019-20 season, as Artistic Partner of the Trondheim Soloists, Weilerstein joined the Norwegian orchestra in London, Munich and Bergen for performances including Haydn's two cello concertos, as featured on their acclaimed 2018 release, Transfigured Night. She also performed ten more concertos by Schumann, Saint-Saëns, Elgar, Strauss, Shostakovich, Britten, Barber, Bloch, Matthias Pintscher and Thomas Larcher, with the London Symphony Orchestra, Zurich's Tonhalle Orchestra, Frankfurt Radio Symphony, Gürzenich Orchestra Cologne, Tokyo's NHK Symphony, the New York Philharmonic, and the Houston, Detroit and San Diego symphonies. In recital, besides making solo Bach appearances, she reunited with her frequent duo partner, Inon Barnatan, for Brahms and Shostakovich at London's Wigmore Hall, Milan's Sala Verdi and Amsterdam's Concertgebouw. To celebrate Beethoven's 250th anniversary, she and the Israeli pianist performed the composer's five cello sonatas in Cincinnati and Scottsdale, and joined Guy Braunstein and the Dresden Philharmonic for Beethoven's Triple Concerto, as heard on the duo's 2019 Pentatone recording with Stefan Jackiw, Alan Gilbert and the Academy of St. Martin in the Fields.   Committed to expanding the cello repertoire, Weilerstein is an ardent champion of new music. She has premiered two important new concertos, giving Pascal Dusapin's Outscape “the kind of debut most composers can only dream of” (Chicago Tribune) with the co-commissioning Chicago Symphony in 2016 and proving herself “the perfect guide” (Boston Globe) to Matthias Pintscher's cello concerto un despertar with the co-commissioning Boston Symphony the following year. She has since reprised Dusapin's concerto with the Stuttgart and Paris Opera Orchestras and Pintscher's with the Gürzenich Orchestra Cologne and with the Danish Radio Symphony and Cincinnati Symphony, both under the composer's leadership. It was also under Pintscher's direction that she gave the New York premiere of his Reflections on Narcissus at the New York Philharmonic's inaugural 2014 Biennial, before reuniting with him to revisit the work at London's BBC Proms. She has worked extensively with Osvaldo Golijov, who rewrote Azul for cello and orchestra for her New York premiere performance at the opening of the 2007 Mostly Mozart Festival. Since then she has played the work with orchestras around the world, besides frequently programming his Omaramor for solo cello. Grammy nominee Joseph Hallman has written multiple compositions for her, including a cello concerto that she premiered with the St. Petersburg Philharmonic and a trio that she premiered on tour with Barnatan and clarinetist Anthony McGill. At the 2008 Caramoor festival, she premiered Lera Auerbach's 24 Preludes for Violoncello and Piano with the composer at the keyboard, and the two subsequently reprised the work at the Schleswig-Holstein Festival, Washington's Kennedy Center and for San Francisco Performances.   Weilerstein's recent Bach and Transfigured Night recordings expand her already celebrated discography. Earlier releases include the Elgar and Elliott Carter cello concertos with Daniel Barenboim and the Staatskapelle Berlin, named “Recording of the Year 2013” by BBC Music, which made her the face of its May 2014 issue. Her next album, on which she played Dvořák's Cello Concerto with the Czech Philharmonic, topped the U.S. classical chart, and her 2016 recording of Shostakovich's cello concertos with the Bavarian Radio Symphony and Pablo Heras-Casado proved “powerful and even mesmerizing” (San Francisco Chronicle). She and Barnatan made their duo album debut with sonatas by Chopin and Rachmaninoff in 2015, a year after she released Solo, a compilation of unaccompanied 20th-century cello music that was hailed as an “uncompromising and pertinent portrait of the cello repertoire of our time” (ResMusica, France). Solo's centerpiece is Kodály's Sonata for Solo Cello, a signature work that Weilerstein revisits on the soundtrack of If I Stay, a 2014 feature film starring Chloë Grace Moretz in which the cellist makes a cameo appearance as herself.   Weilerstein has appeared with all the major orchestras of the United States, Europe and Asia, collaborating with conductors including Marin Alsop, Daniel Barenboim, Jiří Bělohlávek, Semyon Bychkov, Thomas Dausgaard, Sir Andrew Davis, Gustavo Dudamel, Sir Mark Elder, Alan Gilbert, Giancarlo Guerrero, Bernard Haitink, Pablo Heras-Casado, Marek Janowski, Paavo Järvi, Lorin Maazel, Cristian Măcelaru, Zubin Mehta, Ludovic Morlot, Yannick Nézet-Séguin, Peter Oundjian, Rafael Payare, Donald Runnicles, Yuri Temirkanov, Michael Tilson Thomas, Osmo Vänskä, Joshua Weilerstein, Simone Young and David Zinman. In 2009, she was one of four artists invited by Michelle Obama to participate in a widely celebrated and high-profile classical music event at the White House, featuring student workshops hosted by the First Lady and performances in front of an audience that included President Obama and the First Family. A month later, Weilerstein toured Venezuela as soloist with the Simón Bolívar Symphony Orchestra under Dudamel, since when she has made numerous return visits to teach and perform with the orchestra as part of its famed El Sistema music education program.   Born in 1982, Alisa Weilerstein discovered her love for the cello at just two and a half, when she had chicken pox and her grandmother assembled a makeshift set of instruments from cereal boxes to entertain her. Although immediately drawn to the Rice Krispies box cello, Weilerstein soon grew frustrated that it didn't produce any sound. After persuading her parents to buy her a real cello at the age of four, she developed a natural affinity for the instrument and gave her first public performance six months later. At 13, in 1995, she made her professional concert debut, playing Tchaikovsky's “Rococo” Variations with the Cleveland Orchestra, and in March 1997 she made her first Carnegie Hall appearance with the New York Youth Symphony. A graduate of the Young Artist Program at the Cleveland Institute of Music, where she studied with Richard Weiss, Weilerstein also holds a degree in history from Columbia University. She was diagnosed with type 1 diabetes (T1D) at nine years old, and is a staunch advocate for the T1D community, serving as a consultant for the biotechnology company eGenesis and as a Celebrity Advocate for JDRF, the world leader in T1D research. Born into a musical family, she is the daughter of violinist Donald Weilerstein and pianist Vivian Hornik Weilerstein, and the sister of conductor Joshua Weilerstein. She is married to Venezuelan conductor Rafael Payare, with whom she has a young child.     Visit www.mindoverfinger.com and sign up for my newsletter to get your free guide to a super productive practice using the metronome!  This guide is the perfect entry point to help you bring more mindfulness and efficiency into your practice and it's filled with tips and tricks on how to use that wonderful tool to take your practicing and your playing to new heights! Don't forget to visit the Mind Over Finger Resources' page to check out amazing books recommended by my podcast guests, as well as my favorite websites, cds, the podcasts I like to listen to, and the practice and podcasting tools I use everyday!  Find it here: www.mindoverfinger.com/resources!   And don't forget to join the Mind Over Finger Tribe for additional resources on practice and performing! If you enjoyed the show, please leave a review on iTunes!  I truly appreciate your support!     THANK YOU: Most sincere thank you to composer Jim Stephenson who graciously provided the show's musical theme!  Concerto #1 for Trumpet and Chamber Orchestra – Movement 2: Allegro con Brio, performed by Jeffrey Work, trumpet, and the Lake Forest Symphony, conducted by Jim Stephenson. Also a HUGE thank you to my fantastic producer, Bella Kelly!   MIND OVER FINGER: www.mindoverfinger.com https://www.facebook.com/mindoverfinger/ https://www.instagram.com/mindoverfinger/    

Fisher visits with Richard Weiss of the non-profit DNAAdoption.org. Richard and Fisher talk about the unique issues facing adoptees as well as those who have unexpected DNA test results. Richard explains how his organization helps these people.

For American Heart Month, we're exploring various ways to nurture that all-important organ. In part 1, you'll meet Nathalis and Donna, a client-employee combination that proves when you put a little heart into your work, you get a lot back. In part 2, we talk to Dr. Richard Weiss, Clinical Cardiologist from the University of Pennsylvania Health Center, who details how far the science behind our hearts has come—and how far it still has to go.

It’s the 4th Annual “Roy and Jimmy” Christmas Play! This year’s presentation is the classic  “Rudolph The Red Nosed Reindeer”. Guests: Sean Williams, Steve Harbottle, Richard Weiss, Emma Harbottle, Claudia Cortez, Kathie Harbottle, Amy O’Neill

Host Scott Fisher opens the show with David Allen Lambert, Chief Genealogist of the New England Historic Genealogical Society and AmericanAncestors.org. The guys begin with a crazy tale Fisher unearthed in his recent research that forced a marriage date to be pushed up! David starts “Family Histoire News” with the story about a man whose DNA led him to discover he was, in fact, an African prince. Catch the details. Then, a story was recently published about the history of grave robbers and Native American grave sites. David gives an overview. Then, no one ever expects a man to crawl out of a tomb, but it happened in South America. Hear the crazy details! Fisher then visits with Richard Weiss of the non-profit DNAAdoption.org. Richard and Fisher talk about the unique issues facing adoptees as well as those who have unexpected DNA test results. Richard explains how his organization helps these people and how you can support the group. At RootsTech, Fisher visited with actress Patricia Heaton, best known for her roles in “The Middle” and “Everybody Loves Raymond.” Patricia got the “big reveal” from FamilySearch following her keynote speech at the conference. She talks with Fisher about that family background, as well as the challenges of having more than 100 first cousins! Next, it’s Team Black from BYUtv’s Relative Race! The incredible first episode has already aired, and the twins Kaley and Kristen talk to Fisher about being part of the show and some of their experiences. Finally, Tom Perry from TMCPlace.com talks about things you can do to further protect your old magnetic recordings as your attic begins to heat up. That’s all this week on Extreme Genes, America’s Family History Show!

Shira Ovide, Bloomberg Opinion technology columnist, on SoftBank pressuring WeWork CEO Adam Neumann to step down as its IPO falters. John Authers, Senior Editor for Bloomberg Markets, and Carl Riccadonna, Chief U.S. Economist for Bloomberg Economics, discuss how the Fed has handled the repo ruckus, as well as Bill Dudley's recent controversial op-ed. Corlis Murray, SVP and Head of Engineering at Abbott, discusses creating a blueprint for high school internship programs that helps expose girls to STEM fields. Richard Weiss, Bloomberg reporter in Frankfurt, on the U.K. government deploying the “largest repatriation in peacetime history” to bring home tourists stranded by the collapse of tour operator Thomas Cook. Hosted by Lisa Abramowicz and Paul Sweeney. 

It’s Baltimore. It’s August. It’s hot. In times like this, locals head to their favorite snowball shack to beat the heat. The icy, syrupy, slurpy summertime treats are a beloved tradition in Charm City. The first stop is with Richard Weiss, owner of Koldkiss. For more than 40 years it's offered everything one needs to set up a snowball shack. Then an historic delve into snowballs with Baltimore food blogger, Kara Mae Harris and finally a visit with Eric Miller, general manager of Quality Snowballs in Hampden. Plus, we hear from several satisfied snowball slurpers.

A year after being racially profiled along with fellow black college students in Clayton, Missouri, Teddy Washington and his mother, Denise Washington, talk with St. Louis Public Radio's Shula Neuman. Also joining the discussion is Richard Weiss, whose story about the 2018 incident will appear in this Sunday's edition of the St. Louis Post-Dispatch. His reporting is supported through a grant from the Pulitzer Center.

A first ever before heard interview with legendary mountaineer and philanthropist Sir Edmund Hillary, the first man to stand atop Mount Everest in 1953. Our accomplishments mean very little if we do not feel and express gratitude and humility. Sir Edmund Hillary became the first man to stand atop the world's highest mountain with Tenzing Norgay. His legacy, however, is in all that he gave back to the Sherpa people and the Everest region of Nepal. Also in this episode, in March of this year a terrorist in Christchurch, New Zealand burst into to two mosques and killed 50 innocent people. NZ Prime Minister Jacinda Ardern swiftly moved to deny the man the notoriety he expected by making it known that she would never mention him by name. "He may have sought notoriety but we in New Zealand will give him nothing -- not even his name." Music for the episode comes from the Garcia Birthday Band found on the freemusicarchive. They can be found at gbblive.com. Information on Sir Edmund Hillary's legacy can be found at himalayantrust.org. Info on The Explorers Club can be found at explorers.org.

Host Scott Fisher opens the show with David Allen Lambert, Chief Genealogist of the New England Historic Genealogical Society and AmericanAncestors.org. The guys begin with a crazy tale Fisher unearthed in his recent research that forced a marriage date to be pushed up! David starts “Family Histoire News” with the story about a man whose DNA led him to discover he was, in fact, an African prince. Catch the details. Then, a story was recently published about the history of grave robbers and Native American grave sites. David gives an overview. Then, no one ever expects a man to crawl out of a tomb, but it happened in South America. Hear the crazy details! Fisher then visits with Richard Weiss of the non-profit DNAAdoption.org. Richard and Fisher talk about the unique issues facing adoptees as well as those who have unexpected DNA test results. Richard explains how his organization helps these people and how you can support the group. At RootsTech, Fisher visited with actress Patricia Heaton, best known for her roles in “The Middle” and “Everybody Loves Raymond.” Patricia got the “big reveal” from FamilySearch following her keynote speech at the conference. She talks with Fisher about that family background, as well as the challenges of having more than 100 first cousins! Next, it’s Team Black from BYUtv’s Relative Race! The incredible first episode has already aired, and the twins Kaley and Kristen talk to Fisher about being part of the show and some of their experiences. Finally, Tom Perry from TMCPlace.com talks about things you can do to further protect your old magnetic recordings as your attic begins to heat up. That’s all this week on Extreme Genes, America’s Family History Show!

Paul Gallant and Richard Weiss discuss grandparenting and the book “The Grand Journey: Lessons Learned While Navigating Wild Animals and Wilder Times with our Grandkids.”

No matter how you slice it target date funds continue to play a larger role each year in the conversation around workplace retirement plan outcomes.  However, some of the decisions that plan sponsors and fiduciaries make on their target date funds are not evolving as quickly as maybe they should.  When I discuss with employers how they selected their target date strategy often times I hear answers like, they had the best performance, they were inexpensive or they were the one our provider offered.  While these details and others are important in selecting a target date strategy that will match your employee demographics and needs, there is much more that can and should be explored.  To help inform that conversation and illustrate how two very successful target date strategies can take very different approaches I happy to welcome back Rich Weiss, the CIO for Multi-Asset Strategies at American Century and Jerome Clark, a Portfolio Manager in the Asset Allocation Group at T. Rowe Price.  As portfolio managers of their respective firms target date strategies, there are certain things that both Rich and Jerome agree on but much more that they take very different approaches to or have very different opinions on.  Not only was this a ton of fun to have both guys on the podcast, but it illustrates just how important it is to get beyond the numbers when evaluating target date investments and to ensure you understand their process, beliefs and strategies.  Guest Bios Jerome Clark is a portfolio manager in the T. Rowe Price Asset Allocation Group and co-manages the firm's Asset Allocation Target Date Strategies and oversees the College Savings Plan portfolios. He is a member of the firm's Asset Allocation Committee and a vice president of T. Rowe Price Group, Inc. Mr. Clark has 25 years of investment experience, all of which have been at T. Rowe Price. He joined the firm in 1992 as a quantitative analyst in the Fixed Income Division. He was the portfolio manager of the U.S. Treasury Long-Term Bond Strategy from 1998 through 2003 and began managing asset allocation portfolios in 2001. Prior to joining T. Rowe Price, Mr. Clark was a captain in the United States Marine Corps and spent three years as a mathematics instructor at the U.S. Naval Academy. Mr. Clark earned a B.S. in mathematics from the U.S. Naval Academy, an M.S. in operations research from the Naval Postgraduate School, and an M.B.A. in finance from Johns Hopkins University. He has also earned the Chartered Financial Analyst designation. ​Richard Weiss is a Senior Vice President and Chief Investment Officer, Multi-Asset Strategies for American Century Investments.  He is the co-portfolio manager for the firm’s asset allocation strategies, including Strategic Allocation, Global Allocation and One Choice Portfolios®. He also serves as a member of the firm’s Investment Oversight and Asset Allocation Committees, which is responsible for establishing investment policy and reviewing investment decisions for all of our asset allocation products. ​Prior to joining the firm in 2010, Rich was executive vice president and chief investment officer of City National Bank, where he was responsible for their $12 billion investment management group and directed investment policy and strategy. Previously, he was executive vice president and chief investment officer at Sanwa Bank California, where he managed all aspects of their investment department. Earlier in his career, Rich held senior investment positions at Vantage Global Advisors, TSA Capital Management, PaineWebber and Mellon Bank. He has worked in the investment industry since 1984. ​Rich holds a bachelor’s degree in finance from the Wharton School of the University of Pennsylvania and an MBA from the University of Chicago. He has authored several academic papers and is well known for his advanced work in the field of global investing. 401(k) Fridays Podcast Overview Struggling with a fiduciary issue, looking for strategies to improve employee retirement outcomes or curious about the impact of current events on your workplace retirement plan? We've had conversations with retirement industry leaders to address these and other relevant topics! You can easily explore over 100 prior on-demand audio interviews here. Don't forget to subscribe as we release a new episode each Friday!

Matt DeCample sits down with Richard Weiss, longtime director of the Arkansas Department of Finance and Administration, to talk about the joys and tragedies of growing up as a missionary kid in Africa, trying to adjust to life in the United States as a young adult, and the important of good government.

Matt DeCample sits down with Richard Weiss, longtime director of the Arkansas Department of Finance and Administration, to talk about the joys and tragedies of growing up as a missionary kid in Africa, trying to adjust to life in the United States as a young adult, and the important of good government.

Rebecca Waldecker ist Professorin für Algebra an der Martin-Luther-Universität Halle-Wittenberg. Sie besuchte Karlsruhe aus Anlass einer Konferenz zu Ehren von Richard Weiss und Gudrun nutzte die Gelegenheit, um mit ihr über das Faszinosum und die Nützlichkeit von Primzahlen und ihr Forschungsgebiet der Gruppentheorie zu sprechen. In der Vergangenheit gab es verschiedene Definitionen für Primzahlen, die sich über die Zeit zu dem heute gebräuchlichen geschärft haben: Eine Primzahl ist eine natürliche Zahl, die genau zwei verschiedene natürliche Teiler hat - sich selbst und 1.Die Zahl 1 ist damit keine Primzahl, aber z.B. ist die Zahl 2 prim sowie die Zahlen 3, 5, 7, 11, 13, 17, 19 usw. Ein grundlegendes Resultat besagt, dass sich alle natürlichen Zahlen eindeutig in Produkte von Primzahlen aufteilen lassen. Zahlen, die selbst nicht prim sind, nennt man deshalb zerlegbar bzw. zusammengesetzt, weil man sie mit Hilfe dieser Darstellung in die zugehörigen Primfaktoren aufteilen kann bzw. man diese als Grundbausteine der natürlichen Zahlen ansehen kann. Es gibt in diesem Zusammenhang viele interessante Fragen. Zum Beispiel: Wie viele Primzahlen gibt es? Gibt es beliebig große Primzahlzwillinge, d.h. zwei Primzahlen, die voneinander nur den Abstand 2 haben (wie z.B. 11 und 13)? Wie kann ich eine Zahl als Primzahl erkennen? Wie kann ich für jede Zahl (effektiv) die Zerlegung in Primfaktoren berechnen? Interessant ist, dass diese Fragen, die doch eher theoretisch und fast schon spielerisch wirken, heute eine große Relevanz erhalten, weil sich alle gebräuchlichen digitalen Verschlüsselungsverfahren (z.B. beim online-Banking) großer Primzahlen bedienen (je größere Primzahlen man verwenden kann, desto sicherer ist die zugehörige Verschlüsselung). Das liegt daran, dass es im Allgemeinen tatsächlich eine recht lange Rechenzeit braucht, um große Zahlen in mögliche Primfaktoren zu zerlegen. Wenn man sich jedoch davon löst, Primzahlen und Teiler nur auf natürliche Zahlen zu beziehen, wird die Welt noch ein wenig interessanter. Besonders einfach und fast offensichtlich ist es bei der Ausweitung auf ganze Zahlen. In den ganzen Zahlen gibt es mehr Teiler: Zum Beispiel hat die Zahl 3 dort (neben 3 und 1) auch noch die Teiler -1 und -3. Man muss dann entscheiden, welches die Grundbausteine für ganze Zahlen sein sollen. Noch etwas allgemeiner ausgedrückt: Wenn der Begriff der Primzahl auf andere Zahlbereiche verallgemeinert wird, dann gibt es zwei Eigenschaften, die man als charakterisch für "prim" ansehen kann: Einerseits die "Unzerlegbarkeit", also die Eigenschaft, nur die offensichtlichen Teiler zu besitzen. Primzahlen haben aber auch die Eigenschaft (im Bereich der ganzen Zahlen), dass, wenn sie ein Produkt von Zahlen teilen, sie automatisch mindestens einen der Faktoren teilen. Auch diese Eigenschaft kann man zur Verallgemeinerung der Eigenschaft "prim" benutzen. Häufig ist es so, dass in der Übertragung der Idee auf Objekte, die die Struktur eines algebraischen Rings haben (d.h. grob gesprochen, man "rechnet" in ihnen mehr oder weniger so, wie wir es von den ganzen Zahlen kennen) die Unzerlegbarkeit mit dem Begriff "irreduzibel" verallgemeinert wird und dass die andere Eigenschaft (wenn man ein Produkt teilt, dann auch mindestens einen der Faktoren) mit "prim" oder "Primelement" verallgemeinert wird. In manchen Zahlbereichen fallen diese Begriffe zusammen. Zum Beispiel ist das bei den ganzen Zahlen so und bei den im Gespräch erwähnten Ganzen Gaußschen Zahlen. Die Ganzen Gaußschen Zahlen werden aus allen Punkten mit ganzzahligen Koordinaten in der Gaußschen Zahlenebene gebildet. Diese Ebene ist eine geometrische Interpretation der Menge der komplexen Zahlen - die beiden Achsen geben Real- und Imaginärteil der jeweiligen komplexen Zahl an. Wählt man alle ganzzahligen Punkte, so ergibt das eine Struktur, die geometrisch betrachtet ein Gitter ist, und die algebraisch betrachtet den ganzen Zahlen nicht unähnlich ist. Allerdings wird die Multiplikation etwas interessanter, deshalb ändern sich die Eigenschaften von Primzahlen im Ring der Ganzen Gaussschen Zahlen. 2 ist dort keine Primzahl, sondern hat neben den offensichtlichen Teilern 2,-2,1,-1,i,-i,2i,-2i auch noch die Teiler 1+i, 1-i und noch einige mehr. Alle Primzahlen, die beim Teilen durch 4 in den Rest 3 lassen, bleiben prim in . Zum Beispiel 3, 7 und 11. Alle Primzahlen, die beim Teilen durch 4 in den Rest 1 lassen, sind nicht mehr prim in , sondern bekommen dort interessante zusätzliche Teiler. Das liegt daran, dass diese Zahlen sich als Summe von zwei Quadraten schreiben lassen. Streng genommen geht es hier nicht um die Eigenschaft, prim zu sein, sondern um die Eigenschaft, irreduzibel zu sein (siehe oben). Aber im Ring der Ganzen Gaussschen Zahlen fallen diese Begriffe zusammen. Wer sich dafür interessiert, findet beispielsweise beim Suchen mit den Stichworten Zwei-Quadrate-Satz von Fermat und Normfunktion bei den Ganzen Gaußschen Zahlen viele weitere Informationen und Details. Für die Herleitung von effektiven Verfahren, die Primzahlen herausfischen (Primzahlsieb), ist es mitunter nützlich, auf bestimmte Eigenschaften von Primzahlen zurückzugreifen, statt stur alle Teiler zu probieren - von denen gibt es schon für mittelgroße Zahlen nämlich ganz schön viele und es wird selbst mit Hilfe schneller Computer recht zäh. Eine solche Eigenschaft ist im kleinen Satz von Fermat formuliert: Ist p eine Primzahl und ist a eine ganze Zahl, so gilt: und a haben beim Teilen durch p den gleichen Rest. Falls a nicht durch p teilbar ist, dann gibt es noch eine andere Version: hat beim Teilen durch p genau den Rest 1. Dies kann man zur Erkennung von Primzahlen ausnutzen: Ist n eine natürliche Zahl, die man auf Primalität untersuchen möchte, so wählt man sich zufällig eine Zahl a, die echt zwischen 1 und n liegt und die teilerfremd zu n ist (falls das nicht möglich ist, dann ist n=2 und man kann den Test sofort beenden). Nun haben wir also a und n und berechnen . Falls beim Teilen durch n dann der Rest 1 herauskommt, dann ist das Testergebnis "n ist wahrscheinlich prim.". Andernfalls ist das Testergebnis "n ist zusammengesetzt." Das Ergebnis "zusammengesetzt" ist immer richtig, aber das Ergebnis "prim" ist manchmal falsch. Bei den sogenannten Pseudoprimzahlen erscheint für manche Werte von a die Ausgabe "prim", obwohl die Zahl in Wirklichkeit zusammengesetzt ist. Noch schlimmer: Bei den sogenannten Carmichael-Zahlen ist es sogar so, dass für jede mögliche Zahl a, die man sich für den Test wählen könnte (mit den Einschränkungen von oben), der Test das Ergebnis "prim" ausgibt, obwohl die Zahl in Wirklichkeit zusammengesetzt ist. Solche "Unfälle" haben dazu geführt, dass man nach feineren Tests gesucht hat, die weniger Fehler machen. Ein Beispiel ist der Miller-Rabin-Test. Der erste Schritt ist dabei so ähnlich wie beim Fermat-Test, aber es gibt danach noch einen zweiten Schritt. Auf der Seite http://www.visual.wegert.com von Elias Wegert findet man viele wunderbare Illustrationen, manche davon haben mit Primzahlen zu tun. Hier sind noch mehr Tipps zum Stoebern und Weiterlesen: Literatur und weiterführende Informationen Chris K. Caldwell: The List of Largest Known Primes Home Page R. Waldecker, L. Rempe-Gillen: Primzahltests für Einsteiger, 2. Auflage. Springer, 2015. Auch in englisch erhältlich: Primality testing for beginners, Januar 2014 in der Serie Student Mathematical Library der AMS. E. Wegert: Visual Complex Functions, Birkhäuser, 2012. Agrawal, M., Kayal, N. und Saxena, K.: PRIMES is in P, Annals of Math. 160 (2004), No. 2, 781 - 793. Hardy, G.H.: A mathematician's apology, Cambridge University Press, 1992. Crandall, R. und Pomerance, C.: Prime Numbers: A computational perspective, Springer, 2005. Dietzfelbinger, M.: Primality Testing in Polynomial Time: from randomized algorithms to PRIMES is in P, Springer, 2004. Podcasts S.Ritterbusch: Digitale Währungen, Gespräch mit G. Thäter im Modellansatz Podcast, Folge 32, Fakultät für Mathematik, Karlsruher Institut für Technologie (KIT), 2014. http://modellansatz.de/digitale-waehrungen F. Januszewski: L-Funktionen, Gespräch mit G. Thäter im Modellansatz Podcast, Folge 55, Fakultät für Mathematik, Karlsruher Institut für Technologie (KIT), 2015. http://modellansatz.de/l-funktionen F. Schmidt: RSA-Faktorisierung, Gespräch mit G. Thäter im Modellansatz Podcast, Folge 70, Fakultät für Mathematik, Karlsruher Institut für Technologie (KIT), 2015. http://modellansatz.de/rsa-faktorisierung