When Chief Rabbi Ephraim Mirvis went to the Limmud conference two years ago, he opened the door for other United Synagogue rabbis who had hesitated over whether the cross-communal event was acceptable. The chief won't be attending this year; he is making a trip to India. But it seems the US has gone backwards because just a single of its rabbis appears in the conference programme, Dr Michael Harris, a longtime Limmud supporter. While he will be joined by some Orthodox rabbis from the regions and from the London School of Jewish Studies, it is not a great showing.

Still, there will be plenty of Orthodox teaching talent on offer from abroad. They include three graduates or tutors from Yeshivat Maharat, the New York seminary that ordains women - Wendy Amsellem, Yaffa Epstein and Rabbi Lila Kagedan - as well as Rabbi Ysoscher Katz, the head of Talmud at Yeshivat Chovevei Torah (YCT) in New York, the beating heart of so-called open Orthodoxy.

Open Orthodoxy has been in the news of late. Attacked by the American Orthodox right, it was condemned as deviant only last month by the Conference of European Rabbis, who said they would not recognise open Orthodox rabbis.

Open Orthodoxy revolves around a cluster of institutions which have sprung up over the past 20 years such as Maharat and Chovevei Torah, founded by Rabbi Avi Weiss of Riverdale, or the Jewish Orthodox Feminist Alliance. It is open to the greater public involvement of women in religious life and to grappling with intellectual currents which challenge received thinking.

If the growing arguments lead to schism, "I would be horrified," says Rabbi Katz, who believes debate preferable to denunciation. "There is room for negotiation in a way that addresses all the concerns and requires compromise on both sides."

Sadly, in all communities, there is no leadership in the way there was 20 years ago

But he will be looking for a break from the current polemics at Limmud, where he will deliver a three-part lecture series on how halachah responds to social change. "Torah learning is something that transcends polemics," he says. He will hope to find again the "thirst for Torah" which impressed him when he spoke at the JOFA UK conference and two United synagogues earlier this year.

His background makes him an unlikely representative of open Orthodoxy, since he grew up among the fiercely anti-modernist Satmar Chasidim in New York, until he was thrown out of yeshivah for reading the wrong book. It was the Tanya, the classic work of Lubavitch mysticism - Satmars and Lubavitchers aren't the best of friends.

Eventually he moved out of the Charedi camp altogether, although he says the break was "wrenching". There is much he still deeply cherishes and admires about the Chasidic community of his youth - particularly the "emotional resonance" of its celebration of Shabbat and festivals. "Yiddishkeit in a modern Orthodoxy community has more of a cerebral flavour to it."

Now 47, he combines his teaching at YCT with a role as rabbi of Prospect Heights, which he describes as a "typical modern Orthodox" community in New York. Women open the ark and recite the prayer for Israel or give a dvar Torah on Shabbat morning. Although women-only megillah readings have now taken root within the United Synagogue here, there women are one step ahead and can lead mixed readings of Esther and other megillot.

While he has been quick to take to social media to rebut attacks on open Orthodoxy from the right, such theological controversies may not be foremost in the minds of the ordinary Jew in the pew. He recalls, following the publication of one of his online essays, finding one of his synagogue board members in tears, who told him, "Ysoscher, you are spending your time with these secondary issues that have no significance. Tell me what you are doing to make sure my sons and daughters are going to be shomer Shabbat, keep kashrut and mitzvot."

Orthodoxy, he believes, is in a flux, locked in a game of musical chairs with three trends - Charedi, modern and open Orthodox - vying for two places.The Charedim will leave a void, filled by the right-wing of modern Orthodoxy, while open Orthodoxy will occupy the other chair.

Change is happening amid a vacuum at the top. "Sadly, in all communities, there is no leadership in the way there was 20 years ago, when there was Rabbi Joel Teitelbaum in the Satmar, Aharon Kotler in the Litvishe [Lithuanian] and Rabbi Joseph Soloveitchik in the modern Orthodox," he says. "And the consequence of that is that people are starting to look around outside their own little daled amot [four cubits of halachah]."

If modern Orthodoxy can convince others of its deep-seated commitment to "Torah and Yiddishkeit" more Charedim will gravitate towards it, he says. But it will take "a lot of our work on our part because there is a lot of suspicion around modern Orthodoxy, especially the progressive wing of it".